Signal processor, filter, control circuit for power converter circuit, interconnection inverter system and pwm converter system

ABSTRACT

A signal processor is configured to perform a process equivalent to performing a series of fixed-to-rotating coordinate conversion, a predetermined process and then rotating-to-fixed coordinate conversion, while maintaining linearity and time-invariance. The signal processor performs a process given by the following matrix G: 
     
       
         
           
             G 
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                           F 
                            
                           
                             ( 
                             
                               s 
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                         j 
                       
                     
                   
                 
                 
                   
                     
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     where F(s) is a transfer function representing the predetermined process, ω 0  is a predetermined angular frequency and j is the imaginary unit.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to signal processors, filters, and controlcircuits for controlling output or input of power converter circuits.The present invention also relates to interconnection inverter systemsand PWM converter systems using the control circuits.

2. Description of the Related Art

Interconnection inverter systems convert DC (direct current) power whichis generated by solar cells for example, to AC (alternate current) powerfor supply to electrical power systems. (See JP-A-2009-44897, forexample.)

FIG. 36 is a block diagram for describing a conventional interconnectioninverter system.

The interconnection inverter system A100 converts power generated by aDC power source 1 for supply to a three-phase electrical power system B.Hereinafter, the three phases will be called phase U, phase V and phaseW.

An inverter circuit 2 receives a DC voltage from the DC power source 1,and converts the DC voltage into an AC voltage by way of switchingoperation of switching elements. A filter circuit 3 removes switchingfrequency components contained in the AC voltage outputted from theinverter circuit 2. A voltage transformer circuit 4 increases (ordecreases) the AC voltage from the filter circuit 3 to a system voltageof the electrical power system B. A control circuit 7 receives anelectric current signal detected by a current sensor 5 and a voltagesignal detected by a voltage sensor 6 as inputs, generates PWM signalsbased on these, and outputs the PWM signals to the inverter circuit 2.The inverter circuit 2 performs switching operation of the switchingelements based on the PWM signals from the control circuit 7.

FIG. 37 is a block diagram for describing an internal configuration ofthe control circuit 7.

Electrical current signals of respective phases inputted from thecurrent sensor 5 are then inputted to a three-phase to two-phaseconverter 73.

The three-phase to two-phase converter 73 performs so called three-phaseto two-phase conversion (alpha-beta conversion). The three-phase totwo-phase conversion is a process in which three-phase AC signals areconverted into equivalent two-phase AC signals, by first decomposing thethree-phase AC signal components into two kinds of components in anorthogonal coordinate system (hereinafter called fixed coordinatesystem) composed of a mutually perpendicular two axis called alpha axisand beta axis; and then by adding these components for each of the axes.Thus, the original signal is converted into an AC signal on the alphaaxis and an AC signal on the beta axis. Thus, the three-phase totwo-phase converter 73 converts the three electric current signals Iu,Iv, Iw inputted thereto, to an alpha axis current signal Iα and a betaaxis current signal Iβ, and then outputs these signals to afixed-to-rotating coordinate converter 78.

The conversion process performed in the three-phase to two-phaseconverter 73 is represented by a formula shown below as Equation (1).

$\begin{matrix}{\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix} = {{\sqrt{\frac{2}{3}}\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}\begin{bmatrix}{Iu} \\{Iv} \\{Iw}\end{bmatrix}}} & (1)\end{matrix}$

The fixed-to-rotating coordinate converter 78 performs so calledfixed-to-rotating coordinate conversion (dq conversion). Thefixed-to-rotating coordinate conversion converts two-phase signals inthe fixed coordinate system into two-phase signals in a rotatingcoordinate system. The rotating coordinate system is an orthogonalcoordinate system composed of d axis and q axis which are perpendicularto each other, and rotating in the same direction and at the sameangular velocity as of a fundamental wave of the system voltage in theelectrical power system B. The fixed-to-rotating coordinate converter 78converts alpha axis current signals Iα and beta axis current signals Iβin the fixed coordinate system which are inputted from the three-phaseto two-phase converter 73 into d axis current signals Id and q axiscurrent signals Iq in the rotating coordinate system based on a phase θof the fundamental wave of the system voltage detected by a phasedetector 71, and then outputs the converted signals.

The conversion process performed in the fixed-to-rotating coordinateconverter 78 is represented by a formula shown below as Equation (2).

$\begin{matrix}{\begin{bmatrix}{Id} \\{Iq}\end{bmatrix} = {\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix}}} & (2)\end{matrix}$

An LPF 74 a and an LFP 75 a are low-pass filters, allowing only DCcomponents in the d axis current signals Id and in the q axis currentsignals Iq to pass through, respectively. The fixed-to-rotatingcoordinate conversion converts fundamental wave components in the alphaaxis current signal Iα and the beta axis current signal Iβ into DCcomponents of the d axis current signal Id and q axis current signal Iqrespectively. A PI controller 74 b and a PI controller 75 b each performPI (proportional-integral) control based on the DC component values inthe d axis current signals Id and the q axis current signals Iq anddeviations from their respective target values, and then outputcorrection value signals Xd, Xq. Since DC components can be used as thetarget values, the PI controller 74 b and the PI controller 75 b arecapable of providing highly accurate control.

A rotating-to-fixed coordinate converter 79 converts the correctionvalue signals Xd, Xq, which are inputted from the PI controller 74 b andthe PI controller 75 b respectively, into two correction value signalsXα, Xβ in the fixed coordinate system. In other words, it performs areverse conversion process of the process performed by thefixed-to-rotating coordinate converter 78. The rotating-to-fixedcoordinate converter 79 performs so called rotating-to-fixed coordinateconversion (reverse dq conversion), i.e., conversion of the correctionvalue signals Xd, Xq in the rotating coordinate system into correctionvalue signals Xα, Xβ in the fixed coordinate system based on the phaseθ.

The conversion process performed in the rotating-to-fixed coordinateconverter 79 is represented by a formula shown below as Equation (3).

$\begin{matrix}{\begin{bmatrix}{X\; \alpha} \\{X\; \beta}\end{bmatrix} = {\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}{Xd} \\{Xq}\end{bmatrix}}} & (3)\end{matrix}$

A two-phase to three-phase converter 76 converts the correction valuesignals Xα, Xβ which from the rotating-to-fixed coordinate converter 79into three correction value signals Xu, Xv, Xw. The two-phase tothree-phase converter 76 performs so called two-phase to three-phaseconversion process (reverse alpha-beta conversion), i.e., an inverseconversion process of the process performed by the three-phase totwo-phase converter 73.

The conversion process performed in the two-phase to three-phaseconverter 76 is represented by a formula shown below as Equation (4).

$\begin{matrix}{\begin{bmatrix}{Xu} \\{Xv} \\{Xw}\end{bmatrix} = {{\sqrt{\frac{2}{3}}\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}\begin{bmatrix}{X\; \alpha} \\{X\; \beta}\end{bmatrix}}} & (4)\end{matrix}$

A PWM signal generator 77 generates PWM signals based on the correctionvalue signals Xu, Xv, Xw from the two-phase to three-phase converter 76,and outputs the generated signals.

A problem, however, is that designing the control system of the controlcircuit 7 requires tremendous work. Recent interconnection invertersystems must satisfy requirements for very quick response in its controloperation, such as restoring its output within a predetermined amount oftime upon momentary voltage drop. In order to design the control systemso as to satisfy such requirements as the above, the LPF 74 a and theLFP 75 a must be given optimal parameters, and the PI controller 74 band the PI controller 75 b must be designed to have optimizedproportional and integral gains. However, since the fixed-to-rotatingcoordinate converter 78 and the rotating-to-fixed coordinate converter79 perform nonlinear time-varying processes, it was not possible todesign the control system by using a linear control theory. Further,system analysis was not possible, either, since the control systemincludes nonlinear time-varying processing.

SUMMARY OF THE INVENTION

The present invention has been proposed under the above-describedcircumstances, and it is therefore an object of the present invention toprovide a signal processor configured to perform a process which isequivalent to performing a set of the fixed-to-rotating coordinateconversion, a predetermined process and the rotating-to-fixed coordinateconversion, while maintaining linearity and time-invariance in theprocess.

A first aspect of the present invention provides a signal processorwhich generates an output signal by performing signal processing to aninput signal by a first transfer function. The first transfer functionis expressed by

${G_{l}(s)} = \frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{2}$

where F(s) represents a transfer function expressing a predeterminedprocess, ω₀ represents a predetermined angular frequency, and jrepresents the imaginary unit.

A second aspect of the present invention provides a signal processorwhich outputs a first output signal and a second output signal inresponse to an input of a first input signal and a second input signal.In the signal processor, the first input signal is processed by a firsttransfer function, the second input signal is processed by a secondtransfer function, and two results are added together to obtain thefirst output signal. Also, the first input signal is processed by athird transfer function, the second input signal is processed by thefirst transfer function, and two results are added together to obtainthe second output signal. The first transfer function, the secondtransfer function and the third transfer function are expressedrespectively by:

${G_{1}(s)} = \frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{2}$${G_{2}(s)} = {\pm \frac{{F\left( {s + {j\; \omega_{0}}} \right)} - {F\left( {s - {j\; \omega_{0}}} \right)}}{2j}}$${G_{3}(s)} = {\overset{\_}{+}\frac{{F\left( {s + {j\; \omega_{0}}} \right)} - {F\left( {s - {j\; \omega_{0}}} \right)}}{2j}}$

where F(s) represents a transfer function expressing a predeterminedprocess, ω₀ represents a predetermined angular frequency and jrepresents an imaginary unit.

A third aspect of the present invention provides a signal processorwhich outputs a first output signal, a second output signal and a thirdoutput signal in response to an input of a first input signal, a secondinput signal and a third input signal. In the signal processor, thefirst input signal is processed by a first transfer function, the secondinput signal is processed by a second transfer function, the third inputsignal is processed by a third transfer function, and three results areadded together to obtain the first output signal. Also, the first inputsignal is processed by the second transfer function, the second inputsignal is processed by the first transfer function, the third inputsignal is process by the second transfer function, and three results areadded together to obtain the second output signal. Further, the firstinput signal is processed by the second transfer function, the secondinput signal is processed by the second transfer function, the thirdinput signal is processed by the first transfer function, and threeresults are added together to obtain the third output signal. The firsttransfer function and the second transfer function being expressed by:

${G_{1}(s)} = \frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{3}$${G_{2}(s)} = {- \frac{{F\left( {s + {j\; \omega_{0}}} \right)} - {F\left( {s - {j\; \omega_{0}}} \right)}}{6}}$

where F(s) represents a transfer function expressing a predeterminedprocess, ω₀ represents a predetermined angular frequency, and jrepresents an imaginary unit.

A fourth aspect of the present invention provides a signal processorwhich outputs a first output signal, a second output signal and a thirdoutput signal in response to an input of a first input signal, a secondinput signal and a third input signal. In the signal processor, thefirst input signal is processed by a first transfer function, the secondinput signal is processed by a second transfer function, the third inputsignal is processed by a third transfer function and three results areadded together to obtain the first output signal. Also, the first inputsignal is processed by the third transfer function, the second inputsignal is processed by the first transfer function, the third inputsignal is processed by the second transfer function, and three resultsare added together to obtain the second output signal. Further, thefirst input signal is processed by the second transfer function, thesecond input signal is processed by the third transfer function, thethird input signal is processed by the first transfer function, andthree results are added together to obtain the third output signal. Thefirst transfer function, the second transfer function and the thirdtransfer function are expressed by:

${G_{1}(s)} = \frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{3}$${G_{2}(s)} = \frac{{\left( {{- 1}\overset{\_}{+}{\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; \omega_{0}}} \right)}} + {\left( {{- 1} \pm {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; \omega_{0}}} \right)}}}{6}$${G_{3}(s)} = \frac{{\left( {{- 1} \pm {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; \omega_{0}}} \right)}} + {\left( {{- 1}\overset{\_}{+}{\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; \omega_{0}}} \right)}}}{6}$

where F(s) representing a transfer function expressing a predeterminedprocess, ω₀ representing a predetermined angular frequency and jrepresenting an imaginary unit.

A fifth aspect of the present invention provides a control circuit forcontrolling operation of a plurality of switching units inside a powerconverter circuit by a PWM signal. The control circuit includes thesignal processor according to the first aspect of the present invention;and a PWM signal generator which generates a PWM signal based on anoutput signal from the signal processor obtained by a signal inputthereto of a signal based on an output from or an input to the powerconverter circuit.

According to a preferred embodiment of the present invention, thecontrol circuit further includes a two-phase conversion unit whichconverts a signal based on an output from or an input to the powerconverter circuit into a first signal and a second signal. With thisarrangement, the PWM signal generator generates a PWM signal based on anoutput signal obtained from an input of the first signal to the signalprocessor and an output signal obtained from an input of the secondsignal to the signal processor.

A sixth aspect of the present invention provides a control circuit forcontrolling operation of a plurality of switching units inside a powerconverter circuit by a PWM signal. The control circuit includes atwo-phase conversion unit which converts a signal based on an outputfrom or an input to the power converter circuit into a first signal anda second signal; the signal processor according to the second aspect ofthe present invention; and a PWM signal generator which generates a PWMsignal based on an output signal from the signal processor obtained byan input thereto of the first signal and the second signal.

According to a preferred embodiment of the present invention, the powerconverter circuit relates to a three-phase alternate current, and thetwo-phase conversion unit converts a signal based on a three-phaseoutput from or three-phase input to the power converter circuit into thefirst signal and the second signal.

According to a preferred embodiment of the present invention, the powerconverter circuit relates to a single-phase alternate current. With thisarrangement, the two-phase conversion unit generates a signal based on asingle-phase output from or three-phase input to the power convertercircuit as the first signal, and a signal with a 90-degree phase delayfrom the first signal as the second signal.

A seventh aspect of the present invention provides a control circuit forcontrolling operation of a plurality of switching units inside athree-phase alternate-current related power converter circuit by a PWMsignal. The control circuit includes the signal processor according tothe third aspect or the fourth aspect of the present invention; and aPWM signal generator which generates a PWM signal based on an outputsignal from the signal processor obtained by a signal input thereto of asignal based on an output from or an input to the power convertercircuit.

According to a preferred embodiment of the present invention, the signalprocessor is supplied with deviation signals of the first signal and thesecond signal from their respective target values in place of the firstsignals and the second signal.

According to a preferred embodiment of the present invention, theabove-described “signal based on . . . ” is provided by a deviation ofsaid output from or said input to the power converter circuit from theirrespective target value.

According to a preferred embodiment of the present invention, thepredetermined angular frequency ω₀ is substituted for an angularfrequency nω₀ provided by multiplying the angular frequency ω₀ by anatural number n.

According to a preferred embodiment of the present invention, thecontrol circuit further includes a divergence determination unit fordetermination of a divergent tendency found in control, based on anoutput signal from the signal processor; and a stopping unit forstopping an output of the output signal upon determination of presenceof the divergent tendency by the divergence determination unit.

According to a preferred embodiment of the present invention, thecontrol circuit further includes a divergence determination unit fordetermination of a divergent tendency found in control, based on anoutput signal from the signal processor; and a phase change unit forchanging a phase of the output signal upon determination of presence ofthe divergent tendency by the divergence determination unit.

According to a preferred embodiment of the present invention, thedivergence determination unit determines the presence of the divergenttendency in the control by a value of the output signal surpassing apredetermined threshold value.

According to a preferred embodiment of the present invention, thepredetermined process is given by a transfer function expressed asF(s)=K_(I)/s, where K_(I) represents an integral gain.

According to a preferred embodiment of the present invention, thepredetermined process is given by a transfer function expressed asF(s)=K_(P)+K_(I)/s, where K_(P) and K_(I) represent a proportional gainand an integral gain respectively.

According to a preferred embodiment of the present invention, theabove-described “signal based on . . . ” is provided by a signalobtained by detection of an output current or an input current.

According to a preferred embodiment of the present invention, theabove-described “signal based on . . . ” is provided by a signalobtained by detection of an output voltage or an input voltage.

According to a preferred embodiment of the present invention, a H∞ loopshaping method is utilized in designing a control system.

According to a preferred embodiment of the present invention, the powerconverter circuit is provided by an inverter circuit which generates ACpower to be supplied to an electrical power system, and thepredetermined angular frequency ω₀ is provided by an angular frequencyof a fundamental wave in the electrical power system. An eighth aspectof the present invention provides an interconnection inverter systemwhich includes the control circuit according to said preferredembodiment and an inverter circuit.

According to a preferred embodiment of the present invention, the powerconverter circuit is provided by an inverter circuit for driving amotor, and the predetermined angular frequency ω₀ is providedaccordingly to a rotating speed of the motor.

According to a preferred embodiment of the present invention, the powerconverter circuit is provided by a converter circuit for conversion ofAC power supplied from an electrical power system into DC power, and thepredetermined angular frequency ω₀ is provided by an angular frequencyof a fundamental wave in the electrical power system. A ninth aspect ofthe present invention provides a PWM converter system which includes thecontrol circuit according to said preferred embodiment and a convertercircuit.

A tenth aspect of the present invention provides a filter, whichincludes the signal processor according to one of the first aspectthrough the fourth aspect of the present invention. With thisarrangement, the predetermined process is given by a transfer functionexpressed as F(s)=1/(T·s+1), where T represents a time constant.

An eleventh aspect of the present invention provides a filter whichincludes the signal processor according to one of the first aspect tothe fourth aspect of the present invention. With this arrangement, thepredetermined process is given by a transfer function expressed asF(s)=T·s/(T·s+1), where T represents a time constant.

A twelfth aspect of the present invention provides a phase detectorwhich detects a phase of a fundamental wave component in an AC signal.The phase detector includes the filter according to the tenth aspect orthe eleventh aspect of the present invention, and the predeterminedangular frequency ω₀ is provided by an angular frequency of a in afundamental wave component the AC signal.

Other characteristics and advantages of the present invention willbecome clearer from the following detailed description to be made withreference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram for describing a method of converting aprocess involving fixed-to-rotating and rotating-to-fixed coordinateconversions into a linear time-invariant process.

FIG. 2 is a block diagram, presented by way of matrix, for describing amethod of converting a process which involves fixed-to-rotatingcoordinate conversion and rotating-to-fixed coordinate conversion into alinear time-invariant process.

FIG. 3 is a block diagram for describing a matrix calculation.

FIG. 4 is a block diagram of a process in which fixed-to-rotatingcoordinate conversion is followed by PI control and then byrotating-to-fixed coordinate conversion.

FIG. 5 is a block diagram of a process in which fixed-to-rotatingcoordinate conversion is followed by I control and then byrotating-to-fixed coordinate conversion.

FIG. 6 is a block diagram for describing an interconnection invertersystem according to a first embodiment.

FIG. 7 is a Bode diagram for analyzing transfer functions as elements ofa matrix G_(I).

FIG. 8 is a diagram for describing a positive phase sequence componentsignal and a negative phase sequence component signal.

FIG. 9 is a block diagram for describing a control circuit according toa second embodiment.

FIG. 10 is a diagram for describing a result of a simulation conductedwith the second embodiment.

FIG. 11 is a block diagram for describing a control circuit according toa third embodiment.

FIG. 12 is a Bode diagram for analyzing transfer functions as elementsof a matrix G_(PI).

FIG. 13 is a block diagram for describing a control circuit according toa fourth embodiment.

FIG. 14 is a block diagram for describing a control circuit according toa fifth embodiment.

FIG. 15 is a block diagram for describing a three-phase PWM convertersystem according to a sixth embodiment.

FIG. 16 is a block diagram for describing an interconnection invertersystem according to a seventh embodiment.

FIG. 17 is a diagram for describing a result of a simulation conductedwith an eighth embodiment.

FIG. 18 is a diagram for describing a result of an experiment conductedwith the eighth embodiment.

FIG. 19 is a table for describing a result of an experiment conductedwith the eighth embodiment.

FIG. 20 is a block diagram for describing a control circuit according toa ninth embodiment.

FIG. 21 is a Bode diagram showing a transfer function before and afterinterconnection.

FIG. 22 is a diagram for describing a harmonic compensation controlleraccording to a tenth embodiment.

FIG. 23 is a diagram for describing another example of the harmoniccompensation controller according to the tenth embodiment.

FIG. 24 is a block diagram for describing a motor driving unit accordingto an eleventh embodiment.

FIG. 25 is a block diagram for describing a single-phase interconnectioninverter system according to a twelfth embodiment.

FIG. 26 is a block diagram for describing a single-phase interconnectioninverter system according to a thirteenth embodiment.

FIG. 27 is a block diagram for describing a control circuit according toa fourteenth embodiment.

FIG. 28 is a block diagram of a process in which fixed-to-rotatingcoordinate conversion is followed by low-pass filter process and then byrotating-to-fixed coordinate conversion.

FIG. 29 is a Bode diagram for analyzing transfer functions as elementsof a matrix G_(LPF).

FIG. 30 is a diagram showing a block configuration example of a phasedetector according to a fifteenth embodiment.

FIG. 31 is a block diagram of a process in which fixed-to-rotatingcoordinate conversion is followed by a high-pass filtering process andthen by rotating-to-fixed coordinate conversion.

FIG. 32 is a Bode diagram for analyzing transfer functions as elementsof a matrix G_(HPF).

FIG. 33 is a block diagram for describing an internal configuration of afundamental wave extractor according to a sixteenth embodiment.

FIG. 34 is a diagram showing frequency characteristics of thefundamental wave extractor according to the sixteenth embodiment.

FIG. 35 is a diagram showing a block configuration of a phase detectoraccording to a seventeenth embodiment.

FIG. 36 is a block diagram for describing a conventional typicalinterconnection inverter system.

FIG. 37 is a block diagram for describing an internal configuration of acontrol circuit.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the present invention will be described below withreference to the drawings.

First, description will cover a method of converting a process whichinvolves fixed-to-rotating coordinate conversion and rotating-to-fixedcoordinate conversion into a linear time-invariant process.

FIG. 1( a) is a diagram for describing a process involvingfixed-to-rotating coordinate conversion and rotating-to-fixed coordinateconversion operations. In this process, first, signals α and β areconverted into signals d and q by fixed-to-rotating coordinateconversion. The signals d and q undergo respective processes eachrepresented by a predetermined transfer function F(s), and are outputtedas signals d′ and q′. Next, the signals d′ and q′ are converted intosignals α′ and β′ by rotating-to-fixed coordinate conversion. Anonlinear time-variant process in FIG. 1( a) is transformed into alinear time-invariant process using a transfer function matrix G shownin FIG. 1( b).

The fixed-to-rotating coordinate conversion in FIG. 1( a) is representedby a formula expressed by Equation (5) shown below whereas therotating-to-fixed coordinate conversion is represented by a formulaexpressed by Equation (6) shown below.

$\begin{matrix}{\begin{bmatrix}d \\q\end{bmatrix} = {\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}\alpha \\\beta\end{bmatrix}}} & (5) \\{\begin{bmatrix}\alpha^{\prime} \\\beta^{\prime}\end{bmatrix} = {\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}d^{\prime} \\q^{\prime}\end{bmatrix}}} & (6)\end{matrix}$

Therefore, the process in FIG. 1( a) can be expressed by using matricesas shown in FIG. 2( a). Calculating the product of the three matrices inFIG. 2( a), and transforming the obtained matrix into a lineartime-invariant matrix provides a matrix G in FIG. 1( b). In thisprocess, rotating-to-fixed and fixed-to-rotating coordinate conversionmatrices are converted into products of matrices before performing thecalculations.

The fixed-to-rotating coordinate conversion matrix can be converted intoa matrix product shown on the right side of Equation (7) below.

$\begin{matrix}{\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix} = {{T\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}}} & (7)\end{matrix}$

where, j is the imaginary unit, exp( ) is an exponential of the base ofnatural logarithm, e, and

${T = \begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}},{T^{- 1} = \begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}$

where, T⁻¹ represents an inverse matrix of T.

$\begin{matrix}{{{T\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}} = {{\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & {{- j}\; {\exp \left( {j\; \theta} \right)}} \\{\exp \left( {{- j}\; \theta} \right)} & {j\; {\exp \left( {{- j}\; \theta} \right)}}\end{bmatrix}}} \\{= \begin{bmatrix}\frac{\begin{matrix}{{\exp \left( {j\; \theta} \right)} +} \\{\exp \left( {{- j}\; \theta} \right)}\end{matrix}}{2} & {\frac{\begin{matrix}{{{- \exp}\left( {j\; \theta} \right)} +} \\{\exp \left( {{- j}\; \theta} \right)}\end{matrix}}{2}j} \\{\frac{\begin{matrix}{{\exp \left( {j\; \theta} \right)} -} \\{\exp \left( {{- j}\; \theta} \right)}\end{matrix}}{2}j} & \frac{\begin{matrix}{{\exp \left( {j\; \theta} \right)} +} \\{\exp \left( {{- j}\; \theta} \right)}\end{matrix}}{2}\end{bmatrix}}\end{matrix}$

Here, substituting cos θ+j sin θ for exp(jθ) and cos θ−j sin θ forexp(−jθ) according to Euler's formula provides confirmation that:

${{T\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}} = \begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}$

Similarly, the rotating-to-fixed coordinate conversion matrix can beconverted into a matrix product shown on the right side of Equation (8)given below. The central matrix in the matrix product is a lineartime-invariant matrix.

$\begin{matrix}{\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix} = {{T\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}T^{- 1}}} & (8)\end{matrix}$

where, j is the imaginary unit, exp( ) is an exponential of the base ofnatural logarithm, e, and

${T = \begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}},{T^{- 1} = \begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}$

where T⁻¹ is the inverse matrix of T.

$\begin{matrix}{{{T\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}T^{- 1}} = {{\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & {{- j}\; {\exp \left( {{- j}\; \theta} \right)}} \\{\exp \left( {j\; \theta} \right)} & {j\; {\exp \left( {j\; \theta} \right)}}\end{bmatrix}}} \\{= \begin{bmatrix}\frac{\begin{matrix}{{\exp \left( {{- j}\; \theta} \right)} +} \\{\exp \left( {j\; \theta} \right)}\end{matrix}}{2} & {\frac{\begin{matrix}{{{- \exp}\left( {{- j}\; \theta} \right)} +} \\{\exp \left( {j\; \theta} \right)}\end{matrix}}{2}j} \\{\frac{\begin{matrix}{{\exp \left( {{- j}\; \theta} \right)} -} \\{\exp \left( {j\; \theta} \right)}\end{matrix}}{2}j} & \frac{\begin{matrix}{{\exp \left( {{- j}\; \theta} \right)} +} \\{\exp \left( {j\; \theta} \right)}\end{matrix}}{2}\end{bmatrix}}\end{matrix}$

Here, substituting cos θ+j sin θ for exp(jθ) and cos θ−j sin θ forexp(−jθ) according to Euler's formula provides confirmation that:

${\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}T^{- 1}} = \begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}$

Matrix G can be calculated as described by Equation (9) below, by usingEquations (7) and (8) above and calculating the product of the threematrices shown in FIG. 2( a).

$\begin{matrix}\begin{matrix}{G = {{\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}{F(s)} & 0 \\0 & {F(s)}\end{bmatrix}}\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}}} \\{= {{T\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}{T^{- 1}\begin{bmatrix}{F(s)} & 0 \\0 & {F(s)}\end{bmatrix}}{T\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}}} \\{= {{{{{{T\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}\begin{bmatrix}{F(s)} & 0 \\0 & {F(s)}\end{bmatrix}}\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}}\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}}} \\{= {{{{{T\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}\begin{bmatrix}{\frac{1}{2}{F(s)}} & {\frac{1}{2}{F(s)}} \\{\frac{j}{2}{F(s)}} & {{- \frac{j}{2}}{F(s)}}\end{bmatrix}}\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}}} \\{= {{{{T\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}\begin{bmatrix}{F(s)} & 0 \\0 & {F(s)}\end{bmatrix}}\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}}}\end{matrix} & (9)\end{matrix}$

The elements in the first row and the first column of the three centralmatrices in Equation (9) above can be described by a block diagram shownin FIG. 3. The input-output characteristics of the block diagram shownin FIG. 3 are calculated as follows:

$\begin{matrix}{{y(t)} = {{\exp \left( {{- j}\; {\theta (t)}} \right)}{\int_{0}^{t}{{f\left( {t - \tau} \right)}{\exp \left( {j\; {\theta (\tau)}} \right)}{u(\tau)}{\tau}}}}} \\{= {\int_{0}^{t}{{f\left( {t - \tau} \right)}{\exp \left( {- {j\left( {{\theta (t)} - {\theta (\tau)}} \right)}} \right)}{u(\tau)}{\tau}}}}\end{matrix}$

where F(s) is a single-input single-output transfer function which hasan impulse response f(t).

If θ(t)=ω₀t, θ(t)−θ(τ)=ω₀t−ω₀τ=ω₀(t−τ)=θ(t−τ). Therefore, theinput-output characteristic of the block diagram shown in FIG. 3 areequivalent to those of a linear time-invariant system which has impulseresponse f(t) exp(−jω₀t). Laplace transformation of the impulse responsef(t) exp(−jω₀t) provides a transfer function of F(s+jω₀). Similarly, theinput-output characteristics of the block diagram shown in FIG. 3 withexp(−jθ(t)) and exp(jθ(t)) exchanged with each other are theinput-output characteristics of a transfer function of F(s−jω₀).

Therefore, proceeding further with Equation (9) gives the following:

$\begin{matrix}\begin{matrix}{G = {{{{T\begin{bmatrix}{\exp \left( {{- j}\; \theta} \right)} & 0 \\0 & {\exp \left( {j\; \theta} \right)}\end{bmatrix}}\begin{bmatrix}{F(s)} & 0 \\0 & {F(s)}\end{bmatrix}}\begin{bmatrix}{\exp \left( {j\; \theta} \right)} & 0 \\0 & {\exp \left( {{- j}\; \theta} \right)}\end{bmatrix}}T^{- 1}}} \\{{= {{T\begin{bmatrix}{F\left( {s + {j\; \omega_{0}}} \right)} & 0 \\0 & {F\left( {s - {j\; \omega_{0}}} \right)}\end{bmatrix}}T^{- 1}}}} \\{{= {{\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}\begin{bmatrix}{F\left( {s + {j\; \omega_{0}}} \right)} & 0 \\0 & {F\left( {s - {j\; \omega_{0}}} \right)}\end{bmatrix}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}}} \\{{= {\begin{bmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{j}{2} & {- \frac{j}{2}}\end{bmatrix}\begin{bmatrix}{F\left( {s + {j\; \omega_{0}}} \right)} & {- {{jF}\left( {s + {j\; \omega_{0}}} \right)}} \\{F\left( {s - {j\; \omega_{0}}} \right)} & {{jF}\left( {s - {j\; \omega_{0}}} \right)}\end{bmatrix}}}} \\{\begin{bmatrix}\frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{2} & \frac{{F\left( {s + {j\; \omega_{0}}} \right)} - {F\left( {s - {j\; \omega_{0}}} \right)}}{2} \\\frac{{F\left( {s + {j\; \omega_{0}}} \right)} - {F\left( {s - {j\; \omega_{0}}} \right)}}{2j} & \frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{2}\end{bmatrix}}\end{matrix} & (10)\end{matrix}$

Hence, the process in FIG. 2( a) can be converted into a process shownin FIG. 2( b). The process shown in FIG. 2( b) is equivalent to carryingout fixed-to-rotating coordinate conversion, the operation given by apredetermined transfer function F(s), and then rotating-to-fixedcoordinate conversion. In other words, the system of the above-describedprocess is a linear time-invariant system.

Transfer function for the PI (proportional-integral) control controllercan be expressed as F(s)=K_(P)+K_(I)/s, where K_(P) and K_(I)representing proportional and integral gains respectively. Therefore,the process shown in FIG. 4, specifically, the transfer function matrixG_(PI) which represents a process equivalent to carrying outfixed-to-rotating coordinate conversion, PI control, and thenrotating-to-fixed coordinate conversion can be calculated as Equation(11) below by using Equation (10) above:

$\begin{matrix}\begin{matrix}{G_{Pl} = {{\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}{K_{P} + \frac{K_{l}}{s}} & 0 \\0 & {K_{P} + \frac{K_{l}}{s}}\end{bmatrix}}\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}}} \\{= \begin{bmatrix}{\frac{1}{2}\left( {K_{P} + \frac{K_{l}}{s + {j\; \omega_{0}}} + K_{P} + \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)} & {\frac{1}{2j}\left( {K_{P} + \frac{K_{l}}{s + {j\; \omega_{0}}} - K_{P} - \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)} \\{{- \frac{1}{2j}}\left( {K_{P} + \frac{K_{l}}{s + {j\; \omega_{0}}} - K_{P} - \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)} & {\frac{1}{2}\left( {K_{P} + \frac{K_{l}}{s + {j\; \omega_{0}}} + K_{P} + \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)}\end{bmatrix}} \\{= \begin{bmatrix}\frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}\omega_{0}^{2}}}{s^{2} + \omega_{0}^{2}} & \frac{{- K_{l}}\omega_{0}}{s^{2} + \omega_{0}^{2}} \\\frac{K_{l}\omega_{0}}{s^{2} + \omega_{0}^{2}} & \frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}\omega_{0}^{2}}}{s^{2} + \omega_{0}^{2}}\end{bmatrix}}\end{matrix} & (11)\end{matrix}$

Similarly, transfer function of the I (integral) controller can beexpressed as F(s)=K_(I)/s, where K_(I) is the integral gain. Therefore,the process shown in FIG. 5, i.e., the transfer function matrix G_(I)which represents a process equivalent to carrying out fixed-to-rotatingcoordinate conversion, I control and then rotating-to-fixed coordinateconversion can be calculated as Equation (12) below, using Equation (10)above.

$\begin{matrix}\begin{matrix}{G_{l} = {{\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}\frac{K_{l}}{s} & 0 \\0 & \frac{K_{l}}{s}\end{bmatrix}}\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}}} \\{= \begin{bmatrix}{\frac{1}{2}\left( {\frac{K_{l}}{s + {j\; \omega_{0}}} + \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)} & {\frac{1}{2j}\left( {\frac{K_{l}}{s + {j\; \omega_{0}}} - \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)} \\{{- \frac{1}{2j}}\left( {\frac{K_{l}}{s + {j\; \omega_{0}}} - \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)} & {\frac{1}{2}\left( {\frac{K_{l}}{s + {j\; \omega_{0}}} + \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)}\end{bmatrix}} \\{= \begin{bmatrix}\frac{K_{l}s}{s^{2} + \omega_{0}^{2}} & \frac{{- K_{l}}\omega_{0}}{s^{2} + \omega_{0}^{2}} \\\frac{K_{l}\omega_{0}}{s^{2} + \omega_{0}^{2}} & \frac{K_{l}s}{s^{2} + \omega_{0}^{2}}\end{bmatrix}}\end{matrix} & (12)\end{matrix}$

Hereinafter, description will be made for a case where a signalprocessor which performs the process given by the transfer functionmatrix G_(I) expressed by Equation (12) above is used as an electriccurrent controller in a control circuit of an interconnection invertersystem, as a first embodiment of the present invention.

FIG. 6 is a block diagram for describing an interconnection invertersystem according to the first embodiment.

As shown in the figure, an interconnection inverter system A includes aDC power source 1, an inverter circuit 2, a filter circuit 3, a voltagetransformer circuit 4, a current sensor 5, a voltage sensor 6, and acontrol circuit 7.

The DC power source 1 is connected to the inverter circuit 2. Theinverter circuit 2, the filter circuit 3, and the voltage transformercircuit 4 are connected in series in this order, to respective outputlines of the phase U, phase V and phase W outputs, and then to athree-phase AC electrical power system B. The current sensor 5 and thevoltage sensor 6 are disposed on the output side of the voltagetransformer circuit 4. The control circuit 7 is connected to theinverter circuit 2. The interconnection inverter system A converts DCpower from the DC power source 1 into AC power, for supply to theelectrical power system B. It should be noted here that theconfiguration of the interconnection inverter system A is not limited tothe above. For example, the current sensor 5 and the voltage sensor 6may be disposed on the input side of the voltage transformer circuit 4,or other sensors may be included for control of the inverter circuit 2.Also, the voltage transformer circuit 4 may be disposed on the inputside of the filter circuit 3, or there may be a configuration which doesnot include the voltage transformer circuit 4, i.e., so calledtransformerless configuration may be utilized. Still further, a DC/DCconverter circuit may be placed between the DC power source 1 and theinverter circuit 2.

The DC power source 1, which outputs DC power, includes solar cells forexample. The solar cells convert energy of the sun light into electricenergy thereby generating DC power. The DC power source 1 outputs thegenerated DC power to the inverter circuit 2. The DC power source 1 isnot limited to those which generate DC power by solar cells. Forexample, the DC power source 1 may be provided by fuel cells, batteries,electrical double layer capacitors, lithium-ion batteries, or anapparatus which outputs DC power by converting AC power from a dieselengine powered electric generator, a micro gas turbine generator, a winddriven turbine power generator, etc.

The inverter circuit 2 converts a DC voltage from the DC power source 1into an AC voltage, and outputs the AC voltage to the filter circuit 3.The inverter circuit 2 is a three-phase inverter provided by a PWMcontrol inverter circuit which includes unillustrated six switchingelements in three sets. The inverter circuit 2 switches ON and OFF eachof the switching elements based on PWM signals from the control circuit7, thereby converting the DC voltage from the DC power source 1 into ACvoltages. However, the inverter circuit 2 is not limited to this, andmay be provided by a multi-level inverter for example.

The filter circuit 3 removes high frequency components generated in theprocess of switching operation from the AC voltages inputted from theinverter circuit 2. The filter circuit 3 includes a low-pass filterimplemented by a reactor and a capacitor. After the high frequencycomponent removal step in the filter circuit 3, the AC voltages areoutputted to the voltage transformer circuit 4. The configuration of thefilter circuit 3 is not limited to the above, and may be provided by anyconventional filter circuit capable of removing high frequencycomponents. The voltage transformer circuit 4 increases or decreases theAC voltage outputted from the filter circuit 3 to a voltage which issubstantially equal to a system voltage.

The current sensor 5 detects an AC current (specifically, an outputcurrent from the interconnection inverter system A) in each phaseoutputted from the voltage transformer circuit 4. The detected currentsignals I (Iu, Iv, Iw) are inputted to the control circuit 7. Thevoltage sensor 6 detects a system voltage in each phase of theelectrical power system B. The detected voltage signals V (Vu, Vv, Vw)are inputted to the control circuit 7. It should be noted here that theoutput voltage from the interconnection inverter system A issubstantially equal to the system voltage.

The control circuit 7 controls the inverter circuit 2, and isimplemented by a microcomputer for example. The control circuit 7generates PWM signals based on the current signals I from the currentsensor 5 and the voltage signals V from the voltage sensor 6, andoutputs the PWM signals to the inverter circuit 2. Based on thedetection signals inputted from each sensor, the control circuit 7generates command value signals as instruction signals for the outputvoltage waveform of the output from the interconnection inverter systemA; then generates pulse signals based on the command value signals; andthen outputs the pulse signals as the PWM signals. Based on the PWMsignals inputted, the inverter circuit 2 performs ON/OFF switchingoperation to each switching element, thereby outputting AC voltageswhich have corresponding waveforms to the command value signals. Thecontrol circuit 7 controls the output current by varying the commandvalue signal waveforms thereby varying the output voltage waveforms ofthe interconnection inverter system A. Through this process, the controlcircuit 7 performs various kinds of feedback control.

FIG. 6 only shows a configuration for output current control. The figuredoes not show other control configurations. Actually, however, thecontrol circuit 7 also performs DC voltage control (i.e., a feedbackcontrol to ensure that the input DC voltage will have a predeterminedvoltage target value), reactive power control (i.e., a feedback controlto ensure that output reactive power will have a predetermined reactivepower target value), etc. It should be noted here that the types ofcontrol performed by the control circuit 7 are not limited to the above.For example, the circuit may also perform output voltage control, activepower control, etc.

The control circuit 7 includes a system matching-fraction generator 72,a three-phase to two-phase converter 73, a current controller 74, atwo-phase to three-phase converter 76, and a PWM signal generator 77.

The system matching-fraction generator 72 receives a voltage signal Vfrom the voltage sensor 6, and generates and outputs system commandvalue signals Ku, Kv, Kw. The system command value signals Ku, Kv, Kwserve as reference signals for command value signals used to define theoutput voltage waveform to be outputted from the interconnectioninverter system A. As will be described later, the system command valuesKu, Kv, Kw undergo a correction process using correction value signalsXu, Xv, Xw, to obtain the command value signals.

The three-phase to two-phase converter 73 is identical with thethree-phase to two-phase converter 73 in FIG. 37, receives the threecurrent signals Iu, Iv, Iw from the current sensor 5 and converts theminto an alpha axis current signal Iα and a beta axis current signal Iβ.The conversion process performed in the three-phase to two-phaseconverter 73 is represented by the formula which was shown earlier asEquation (1).

The current controller 74 receives the alpha axis current signal Iα andthe beta axis current signal Iβ from the three-phase to two-phaseconverter 73 and deviations from respective target values, to generatecorrection value signals Xα, Xβ for the current control. The currentcontroller 74 performs a process represented by the transfer functionmatrix G_(I) of Equation (12). In other words, the controller performs aprocess expressed by Equation (13) below, where the deviations of thealpha axis current signal Iα and the beta axis current signal Iβ fromtheir respective target values are represented by ΔIα and ΔIβ. As forthe angular frequency ω₀, a predetermined value is set as an angularfrequency (for example, ω₀=120π [rad/sec] (60 [Hz])) for the systemvoltage fundamental wave, and the integral gain K_(I) is a pre-designedvalue. Also, the current controller 74 performs a stability marginmaximization process, which includes an adjustment to correct phasedelay in the control loop. The deviations ΔIα, ΔIβ represent the “firstinput signal” and “the second input signal” according to the presentinvention respectively whereas the correction value signals Xα, Xβrepresent “the first output signal” and “the second output signal”according to the present invention respectively.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{X\; \alpha} \\{X\; \beta}\end{bmatrix} = {G_{l}\begin{bmatrix}{\Delta \; I\; \alpha} \\{\Delta \; I\; \beta}\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{K_{l}s}{s^{2} + \omega_{0}^{2}} & \frac{{- K_{l}}\omega_{0}}{s^{2} + \omega_{0}^{2}} \\\frac{K_{l}\omega_{0}}{s^{2} + \omega_{0}^{2}} & \frac{K_{l}s}{s^{2} + \omega_{0}^{2}}\end{bmatrix}\begin{bmatrix}{\Delta \; I\; \alpha} \\{\Delta \; I\; \beta}\end{bmatrix}}}\end{matrix} & (13)\end{matrix}$

In the present embodiment, the alpha axis current target value and thebeta axis current target value are provided by values obtained byrotating-to-fixed coordinate conversion values of the d axis currenttarget value and the q axis current target value respectively. The daxis current target value is provided by a correction value for anunillustrated DC voltage control whereas the q axis current target valueis provided by a correction value for an unillustrated reactive powercontrol. It should be noted here that in cases where three-phase currenttarget values are given, those target values should be subjected tothree-phase/two-phase conversion to obtain the alpha axis current targetvalue and the beta axis current target value. Alternatively, deviationsof the three current signals Iu, Iv, Iw from the three-phase currenttarget values may be calculated first, so that these three deviationsignals should be subjected to three-phase/two-phase conversion forinput to the current controller 74. Also, if the alpha axis currenttarget value and the beta axis current target value are supplieddirectly, the supplied target values may be used directly.

FIG. 7 is a Bode diagram for analyzing transfer functions as elements ofa matrix G_(I). FIG. 7( a) shows a transfer function of the element inthe first row and the first column of the matrix G_(I) (hereinafter willbe denoted as “element (1, 1)”; the same applies to the other elements)and the element (2, 2). FIG. 7( b) shows a transfer function of theelement (1, 2) of the matrix G_(I) whereas FIG. 7( c) shows a transferfunction of the element (2, 1) of the matrix G_(I). FIG. 7 shows a casewhere a system voltage fundamental wave frequency (hereinafter will becalled “center frequency”; in addition, an angular frequency whichcorresponds to the center frequency will be called “center angularfrequency”) is 60 Hz (specifically, in a case where the angularfrequency ω₀=120π), and integral gain K_(I) is “0.1”, “1”, “10” and“100”.

All amplitude characteristics in FIGS. 7( a), (b) and (c) show a peak atthe center frequency, and the amplitude characteristic increases as theintegral gain K_(I) increases. Also, FIG. 7( a) shows a phasecharacteristic, which attains 0 degree at the center frequency. In otherwords, the transfer functions of the element (1, 1) and the element (2,2) of the matrix G_(I) allow signals of the center frequency (centerangular frequency) to pass through without changing their phases. FIG.7( b) shows a phase characteristic, which attains 90 degrees at thecenter frequency. In other words, the transfer function of the element(1, 2) of the matrix G_(I) allows signals of the center frequency(center angular frequency) to pass through with a 90-degree phaseadvance. On the other hand, FIG. 7( c) shows a phase characteristic,which attains −90 degrees at the center frequency. In other words, thetransfer function of the element (2, 1) of the matrix G_(I) allowssignals of the center frequency (center angular frequency) to passthrough with a 90-degree phase delay.

In the present embodiment, the current controller 74 is designed byusing a H∞ loop shaping method, which is a linear control theory, with afrequency weight being provided by the transfer function matrix G_(I).The process performed in the current controller 74 is expressed as atransfer function matrix G_(I), and therefore is a linear time-invariantprocess. Hence, it is possible to perform control system design using alinear control theory.

The current controller 74 must satisfy design specifications requiringthat the output current follows a sine-wave target value, and that theoutput is restored to a predetermined ratio within a predetermined time(quick response) at the time of momentary voltage drop. For the systemoutput to stay perfectly on a given target value, a closed loop systemmust have the same polarity as the target generator, and the closed loopsystem must be an asymptotic stabilization system (internal modelprinciple). The pole of the sine-wave target value is ±jω₀, whereas thepole of the item 1/(s²+ω₀ ²) contained in the transfer function of eachelement of the matrix G_(I) is also ±jω₀. Therefore, the closed loopsystem and the target generator have the same polarity. Also, it ispossible, if a H∞ loop shaping method is used, to design a controller inwhich the closed loop system achieves asymptotic stabilization.Therefore, using a H∞ loop shaping method enables to satisfy the quickresponse conditions easily and to design the most stable control systemwhich meets the design specifications.

It should be noted here that design method to be used in designing thecontrol system is not limited to this. In other words, other linearcontrol theories may be employed for the design. Examples of usablemethods include loop shaping method, optimum control, H∞ control, mixedsensitivity problem, and more.

Returning to FIG. 6, the two-phase to three-phase converter 76 isidentical with the two-phase to three-phase converter 76 in FIG. 37, andconverts the correction value signals Xα, Xβ from the current controller74 into three correction value signals Xu, Xv, Xw. The conversionprocess performed in the two-phase to three-phase converter 76 isrepresented by a formula shown earlier as Equation (4).

The system command value signals Ku, Kv, Kw from the systemmatching-fraction generator 72 and the correction value signals Xu, Xv,Xw from the two-phase to three-phase converter 76 are added to eachother respectively, to obtain command value signals X′u, X′v, X′w, whichare then inputted to the PWM signal generator 77.

The PWM signal generator 77 generates PWM signals Pu, Pv, Pw by trianglewave comparison method based on the command value signals X′u, X′v, X′winputted thereto and a carrier signal which is generated as atriangle-wave signal at a predetermined frequency (e.g. 4 kHz). In thetriangle wave comparison method, each of the command value signals X′u,X′v, X′w are compared to the carrier signal, to generate a pulsesignals. For example, a PWM signal Pu assumes a high level when thecommand value signal X′u is greater than the carrier signal and a lowlevel when it is not, for example. The generated PWM signals Pu, Pv, Pware outputted to the inverter circuit 2.

In the present embodiment, the control circuit 7 performs a control inthe fixed coordinate system without making fixed-to-rotating coordinateconversion nor rotating-to-fixed coordinate conversion. As has beendescribed earlier, the transfer function matrix G_(I) gives a processwhich is equivalent to carrying out fixed-to-rotating coordinateconversion, then I control and then rotating-to-fixed coordinateconversion. Therefore, the current controller 74 which performs theprocess represented by the transfer function matrix G_(I) performs anequivalent process to the process in FIG. 37 performed by thefixed-to-rotating coordinate converter 78, the rotating-to-fixedcoordinate converter 79, and the I control process (implemented by thePI control process performed by the PI controller 74 b and the PIcontroller 75 b in FIG. 37). Also, as shown in each Bode diagram in FIG.7, the transfer function of each element in the matrix G_(I) has anamplitude characteristic which attains a peak at the center frequency.In other words, in the current controller 74, only the center frequencycomponent is a high-gain component. Therefore, there is no need forproviding the LPF 74 a or 75 a in FIG. 37.

Also, since the process performed in the current controller 74 isexpressed as the transfer function matrix G_(I), it is a lineartime-invariant process. The control circuit 7 does not include nonlineartime-varying processes, i.e., the circuit does not includefixed-to-rotating coordinate conversion process or rotating-to-fixedcoordinate conversion process. Hence, the entire current control systemis a linear time-invariant system. Therefore, the arrangement enablescontrol system design and system analysis using a linear control theory.As described, use of the transfer function matrix G_(I) expressed byEquation (12) enables to replace the non-linear process in whichfixed-to-rotating coordinate conversion is followed by I control andthen by rotating-to-fixed coordinate conversion with a lineartime-invariant multi-input multi-output system. This makes it easy toperform system analysis and control system design thereby.

It should be noted here that in the embodiment described above, thecurrent controller 74 performs the process represented by Equation (13).However, each element in the matrix G_(I) may be given a different valuefrom others for its integral gain K_(I). Specifically, the integral gainK_(I) for each element may have a different value from one transferfunction to another. For example, there may be a design to includeadditional characteristics in the alpha axis component such as improvedresponse, improved stability, etc. Another example of adding one morecharacteristic may be to assign “0” to the integral gain K_(I) of theelement (1, 2) and that of the element (2, 1), to control both ofnegative-phase sequence components and negative-phase sequencecomponents. Later, description will be made for cases of controllingboth positive-phase and negative-phase sequence components. It should benoted here that setting a different integral gain K_(I) for each elementdoes not change the phase characteristic of the transfer function whichrepresents each element. Therefore, the transfer function of the element(1, 1) and that of the element (2, 2) allow center frequency signalspass through without changing their phases whereas the transfer functionof the element (1, 2) allows the center frequency signals to passthrough with a 90-degree phase advance, and the transfer function of theelement (2, 1) allows the center frequency signals to pass through witha 90-degree phase delay.

In the first embodiment described thus far, description was made for acase where positive phase sequence component control is performed to thefundamental wave component of the current signals Iu, Iv, Iw. However,the present invention is not limited to this. In addition to thepositive phase sequence component signals in the fundamental wavecomponents, the current signals Iu, Iv, Iw are superimposed withnegative phase sequence component signals. There may be an arrangementwhere control is provided only to these negative phase sequencecomponent signals.

FIG. 8 is a drawing for describing positive phase sequence componentsignals and negative phase sequence component signals. FIG. 8( a) showsa positive phase sequence component signal whereas FIG. 8( b) shows anegative phase sequence component signal.

In FIG. 8( a), arrows in broken lines are vectors u, v, w representingpositive phase sequence components in the fundamental wave component incurrent signals Iu, Iv, Iw. The vectors u, v, w have differentdirections at a 120-degree interval, and are identified in this order inthe clockwise direction, rotating in the counterclockwise direction atan angular frequency of ω₀. When the current signals Iu, Iv, Iw undergothree-phase/two-phase conversion, resulting positive phase sequencecomponents of the fundamental wave component in the alpha axis currentsignal Iα and the beta axis current signal Iβ are indicated bysolid-line arrow vectors α, β. The vectors α, β have a 90-degreeclockwise difference in direction, and are rotating in thecounterclockwise direction at an angular frequency of ω₀.

In other words, the positive phase sequence component in the fundamentalwave component of the alpha axis current signal Iα outputted from thethree-phase to two-phase converter 73 (see FIG. 6) has a 90-degree phaseadvance over the positive phase sequence component in the fundamentalwave component of the beta axis current signal Iβ. Therefore, thepositive phase sequence component in the fundamental wave component ofthe deviation ΔIα from the target value also has a 90-degree phaseadvance over the positive phase sequence component in the fundamentalwave component of the deviation ΔIβ. Performing the process representedby the transfer function of the element (1, 1) in the matrix G_(I) tothe deviation ΔIα does not change the phase of the positive phasesequence component in the fundamental wave component (see FIG. 7( a)).Also, performing the process represented by the transfer function of theelement (1, 2) in the matrix G_(I) to the deviation ΔIβ advances thephase of the positive phase sequence component in the fundamental wavecomponent by 90 degrees (see FIG. 7( b)). Therefore, both phases are nowthe same as the phase of the positive phase sequence component in thefundamental wave component of the deviation ΔIα, which means adding thetwo will make enhancement. On the other hand, performing the processrepresented by the transfer function of the element (2, 1) in the matrixG_(I) to the deviation ΔIα delays the phase of the positive phasesequence component in the fundamental wave component by 90 degrees (seeFIG. 7( c)). Also, performing the process represented by the transferfunction of the element (2, 2) in the matrix G_(I) to the deviation ΔIβdoes not change the phase of the positive phase sequence component inthe fundamental wave component. Therefore, both phases are now the sameas the phase of the positive phase sequence component in the fundamentalwave component of the deviation ΔIβ, which means adding the two willmake enhancement.

The negative phase sequence component is a component in which the phasesequence is reversed from that of the positive phase sequence component.In FIG. 8( b), arrows in broken lines are vectors u, v, w representingnegative phase sequence components in the fundamental wave components incurrent signals Iu, Iv, Iw. The vectors u, v, w have differentdirections at a 120-degree interval, are identified in this order in thecounterclockwise direction, and are rotating in the counterclockwisedirection at an angular frequency of ω₀. When the current signals Iu,Iv, Iw undergo three-phase/two-phase conversion, resulting negativephase sequence component of the fundamental wave component in the alphaaxis current signal Iα and the beta axis current signal Iβ are indicatedby solid-line arrow vectors α, β. The vectors α, β have a 90-degreecounterclockwise difference in direction, and are rotating in thecounterclockwise direction at an angular frequency of ω₀.

In other words, the negative phase sequence component in the fundamentalwave component of the alpha axis current signal Iα outputted from thethree-phase to two-phase converter 73 has a 90-degree phase delay fromthe negative phase sequence component in the fundamental wave componentof the beta axis current signal Iβ. Performing the process representedby the transfer function of the element (1, 1) in the matrix G_(I) tothe deviation ΔIα does not change the phase of the negative phasesequence component in the fundamental wave component. Also, performingthe process represented by the transfer function of the element (1, 2)in the matrix G_(I) to the deviation ΔIβ advances the phase of thenegative phase sequence component in the fundamental wave component by90 degrees. Therefore, the two phases become opposite to each other,which means they cancel each other when the two are added to each other.On the other hand, performing the process represented by the transferfunction of the element (2, 1) in the matrix G_(I) to the deviation ΔIαdelays the phase of the negative phase sequence component in thefundamental wave component by 90 degrees. Also, performing the processrepresented by the transfer function of the element (2, 2) in the matrixG_(I) to the deviation ΔIβ does not change the phase of the negativephase sequence component in the fundamental wave component. Therefore,the two phases become opposite to each other, which means they canceleach other when the two are added to each other. Therefore, the currentcontroller 74 performs positive phase sequence component control of thefundamental wave component but does not perform negative phase sequencecomponent control thereof.

Swapping the element (1, 2) and the element (2, 1) of the transferfunction matrix G_(I) will provide the opposite result of what wasdescribed above, i.e., positive phase sequence components in thefundamental wave component will cancel each other whereas negative phasesequence component will enhance each other. Therefore, negative phasesequence component control in the fundamental wave component can beperformed in the first embodiment by using the transfer function matrixG_(I) matrix in which the element (1, 2) and the element (2, 1) areswapped with each other.

Next, description will cover a case where both of positive-phase andnegative-phase sequence components in the fundamental wave component arecontrolled.

The process represented by the transfer function of the element (1, 1)and the element (2, 2) in the matrix G_(I) allows the positive-phase andthe negative-phase sequence components in the fundamental wave componentto pass through without changing their phases (see FIG. 7( a)).Therefore, it is possible to perform control on both of thepositive-phase and the negative-phase sequence components in thefundamental wave component if the element (1, 2) and the element (2, 1)are “0” in the matrix G_(I) represented by the Equation (12). In thiscase, there is no component enhancement unlike in the case where onlythe positive phase sequence component is controlled (where the matrixG_(I) represented by Equation (12) is utilized), so the integral gainK_(I) must be given a larger value accordingly. Hereinafter, descriptionwill be made for a second embodiment, where both of positive-phase andnegative phase sequence components in the fundamental wave component arecontrolled.

FIG. 9 is a block diagram for describing a control circuit according tothe second embodiment. In FIG. 9, those elements which are identical orsimilar to those included in the control circuit 7 in FIG. 6 areindicated by the same reference codes.

FIG. 9 shows a control circuit 7′, which differs from the controlcircuit 7 (see FIG. 6) according to the first embodiment in that thecurrent controller 74 is replaced by an alpha axis current controller74′ and a beta axis current controller 75′.

The alpha axis current controller 74′ receives a deviation ΔIα betweenthe alpha axis current signal Iα from the three-phase to two-phaseconverter 73 and an alpha axis current signal target value, to generatea correction value signal Xα for the current control. The alpha axiscurrent controller 74′ performs a process represented by K_(I)·s/(s²+ω₀²) which is a transfer function of the element (1, 1) and the element(2, 2) in the matrix G_(I). Also, the alpha axis current controller 74′performs a stability margin maximization process, which includes phaseadjustment to correct a phase delay in the control loop. The deviationΔIα represents the “input signal” according to the present inventionwhereas the correction value signal Xα represents the “output signal”according to the present invention.

The beta axis current controller 75′ receives a deviation ΔIβ betweenthe beta axis current signal Iβ from the three-phase to two-phaseconverter 73 and a beta axis current target value, to generate acorrection value signal Xβ for the current control. The beta axiscurrent controller 75′ performs a process represented by K_(I)·s/(s²+ω₀²) which is a transfer function of the element (1, 1) and the element(2, 2) in the matrix G_(I). Also, the beta axis current controller 75′performs a stability margin maximization process, which includes phaseadjustment to correct a phase delay in the control loop. The deviationΔIβ represents the “input signal” according to the present inventionwhereas the correction value signal Xβ represents the “output signal”according to the present invention.

In the present embodiment, the alpha axis current controller 74′ and thebeta axis current controller 75′ are designed by H∞ loop shaping method,which is based on a linear control theory, with a frequency weight beingprovided by the transfer function K_(I)·s/(s²+ω₀ ²) for each of thecontrollers. The processes performed in the alpha axis currentcontroller 74′ and the beta axis current controller 75′ are expressed bythe transfer function K_(I)·s/(s²+ω₀ ²), and therefore are lineartime-invariant processes. Hence, it is possible to perform controlsystem design using a linear control theory. It should be noted herethat a linear control theory other than the H∞ loop shaping method maybe utilized in the design.

The present embodiment provides the same advantages as offered by thefirst embodiment. The alpha axis current controller 74′ and the betaaxis current controller 75′ may be given different values from eachother for the integral gain K_(I) in their transfer functionK_(I)·s/(s²+ω₀ ²). Specifically, a specific value may be individuallydesigned and used as the integral gain K_(I) for each of the alpha axiscurrent controller 74′ and the beta axis current controller 75′. Forexample, there may be a design to include additional characteristics inthe alpha axis component such as improved response, improved stability,etc.

FIG. 10 is a diagram for describing a result of a simulation conductedwith the second embodiment.

In the simulation, non-balanced distortion was added to the current ofeach phase in the interconnection inverter system A (see FIG. 6), with atarget current set at 20 (A). FIG. 10( a) shows a deviation ΔIα inputtedto the alpha axis current controller 74′ (see FIG. 9), and a deviationΔIβ inputted to the beta axis current controller 75′. FIG. 10( b) showscurrent signals Iu, Iv, Iw detected in an output current of each phaseby the current sensor 5. As shown in FIG. 10( a), the deviation ΔIα andthe deviation ΔIβ became gradually smaller and attained “0”substantially, in 0.14 [s]. Also, as shown in FIG. 10( b), the currentsignals Iu, Iv, Iw became gradually larger and achieved 80-percentvalue, i.e. 16 [A], of the target in 0.05 [s]. Note also, that each ofthe current signals Iu, Iv, Iw has a balanced waveform. Since thenon-balanced distortion has been removed and the positive phase sequencecomponent follows the target value, it is clear that the alpha axiscurrent controller 74′ and the beta axis current controller 75′ controlpositive-phase and negative-phase sequence components appropriately.Also, the control has sufficiently quick response.

In the first and the second embodiments, description was made for caseswhere three current signals Iu, Iv, Iw are converted into an alpha axiscurrent signal Iα and a beta axis current signal Iβ to provide control.However, the present invention is not limited to this. For example,control may be provided through direct use of the three current signalsIu, Iv, Iw. Hereinafter, such a case will be described as a thirdembodiment.

FIG. 11 is a block diagram for describing a control circuit according tothe third embodiment. In this figure, elements which are identical withor similar to those in the control circuit 7 in FIG. 6 are indicated bythe same reference codes.

FIG. 11 shows a control circuit 7″, which differs from the controlcircuit 7 (see FIG. 6) according to the first embodiment in that it doesnot have the three-phase to two-phase converter 73 and the two-phase tothree-phase converter 76, and that the current controller 74″ providesdirect control using the current signals Iu, Iv, Iw.

Since three-phase to two-phase conversion and two-phase to three-phaseconversion are expressed by Equation (1) and Equation (4), a process inwhich the three-phase to two-phase conversion is followed by the processrepresented by the matrix G of the transfer function and then followedby two-phase to three-phase conversion is represented by a transferfunction matrix G′ shown as Equation (14) below:

$\begin{matrix}{\begin{matrix}{G^{\prime} = {{\frac{2}{3}\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{3}{2}}\end{bmatrix}}} \\{= {{{\frac{2}{3}\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}\begin{bmatrix}\frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{2} & \frac{{F\left( {s + {j\; \omega_{0}}} \right)} - {F\left( {s - {j\; \omega_{0}}} \right)}}{2j} \\{- \frac{{F\left( {s + {j\; \omega_{0}}} \right)} - {F\left( {s - {j\; \omega_{0}}} \right)}}{2j}} & \frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{2}\end{bmatrix}} \times \begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}} \\{= \begin{bmatrix}{G_{11}(s)} & {G_{12}(s)} & {G_{13}(s)} \\{G_{21}(s)} & {G_{22}(s)} & {G_{23}(s)} \\{G_{31}(s)} & {G_{32}(s)} & {G_{33}(s)}\end{bmatrix}}\end{matrix}{{where}\text{:}}{{G_{11}(s)} = {{G_{22}(s)} = {{G_{33}(s)} = \frac{{F\left( {s + {j\; \omega_{0}}} \right)} + {F\left( {s - {j\; \omega_{0}}} \right)}}{3}}}}{{G_{12}(s)} = {{G_{23}(s)} = {{G_{31}(s)} = \frac{{\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; \omega_{0}}} \right)}} + {\left( {{- 1} + {\sqrt{3}\; j}} \right) \cdot {F\left( {s - {j\; \omega_{0}}} \right)}}}{6}}}}{{G_{13}(s)} = {{G_{21}(s)} = {{G_{32}(s)} = \frac{{\left( {{- 1} + {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; \omega_{0}}} \right)}} + {\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; \omega_{0}}} \right)}}}{6}}}}} & (14)\end{matrix}$

Therefore, the transfer function matrix G′_(I) representing the processperformed by the current controller 74″ is represented by Equation (15)below:

$\begin{matrix}{{G_{l}^{\prime} = \begin{bmatrix}{G_{l\; 11}(s)} & {G_{l\; 12}(s)} & {G_{l\; 13}(s)} \\{G_{l\; 21}(s)} & {G_{l\; 22}(s)} & {G_{l\; 23}(s)} \\{G_{l\; 31}(s)} & {G_{l\; 32}(s)} & {G_{l\; 33}(s)}\end{bmatrix}}{{where}\text{:}}\begin{matrix}{{G_{l\; 11}(s)} = {{G_{l\; 22}(s)} = {{G_{l\; 33}(s)} = {\frac{1}{3}\left( {\frac{K_{l}}{s + {j\; \omega_{0}}} + \frac{K_{l}}{s - {j\; \omega_{0}}}} \right)}}}} \\{{= {\frac{2}{3} \cdot \frac{K_{l}s}{s^{2} + \omega_{0}^{2}}}}}\end{matrix}\begin{matrix}{{G_{l\; 12}(s)} = {{G_{l\; 23}(s)} = {{F_{l\; 31}(s)} = {\frac{1}{6}\left\{ {{\left( {{- 1} - {\sqrt{3}j}} \right) \cdot \frac{K_{l}}{s + {j\; \omega_{0}}}} + {\left( {{- 1} + {\sqrt{3}j}} \right) \cdot \frac{K_{l}}{s - {j\; \omega_{0}}}}} \right\}}}}} \\{{= {{- \frac{1}{3}} \cdot \frac{K_{l}\left( {s + {\sqrt{3}\omega_{0}}} \right)}{s^{2} + \omega_{0}^{2}}}}}\end{matrix}\begin{matrix}{{G_{l\; 13}(s)} = {{G_{l\; 21}(s)} = {{G_{l\; 32}(s)} = {\frac{1}{6}\left\{ {{\left( {{- 1} + {\sqrt{3}j}} \right) \cdot \frac{K_{l}}{s + {j\; \omega_{0}}}} + {\left( {{- 1} - {\sqrt{3}j}} \right) \cdot \frac{K_{l}}{s - {j\; \omega_{0}}}}} \right\}}}}} \\{{= {{- \frac{1}{3}} \cdot \frac{K_{l}\left( {s - {\sqrt{3}\omega_{0}}} \right)}{s^{2} + \omega_{0}^{2}}}}}\end{matrix}} & (15)\end{matrix}$

The current controller 74″ receives deviations of the three currentsignals Iu, Iv, Iw outputted by the current sensor 5 from theirrespective target values, to generate correction value signals Xu, Xv,Xw for the current control. The current controller 74″ performs theprocess represented by the transfer function matrix G_(I)′ of Equation(15) above. In other words, the controller performs a process expressedby Equation (16) below, where ΔIu, ΔIv, ΔIw represent the deviations ofthe current signals Iu, Iv, Iw from their respective target values. Asfor the angular frequency ω₀, a predetermined value is set as an angularfrequency (for example, ω₀=120π [rad/sec] (60 [Hz])) for the systemvoltage fundamental wave, and the integral gain K_(I) is a pre-designedvalue. Also, the current controller 74″ performs a stability marginmaximization process, which includes phase adjustment to correct a phasedelay in the control loop. The deviations ΔIu, ΔIv, ΔIw represent “thefirst input signal”, “the second input signal”, and “the third inputsignal” respectively according to the present invention whereas thecorrection value signals Xu, Xv, Xw represent “the first output signal”,“the second output signal” and “the third output signal” according tothe present invention.

$\begin{matrix}{\begin{bmatrix}{Xu} \\{Xv} \\{Xw}\end{bmatrix} = {G_{I}^{\prime}\begin{bmatrix}{\Delta \; {Iu}} \\{\Delta \; {Iv}} \\{\Delta \; {Iw}}\end{bmatrix}}} & (16)\end{matrix}$

In the present embodiment, the target values for the current signals Iu,Iv, Iw are provided by values which are obtained by first performingrotating-to-fixed coordinate conversion to a d axis current target valueand a q axis current target value and then performing two-phase tothree-phase conversion to the obtained values. If three-phase currenttarget values are supplied directly, the supplied target values may beused directly. Also, if the alpha axis current target value and the betaaxis current target value are supplied, then the supplied values shouldbe subjected to two-phase to three-phase conversion for use.

In the present embodiment, the current controller 74″ is designed by H∞loop shaping method, which is based on a linear control theory, with afrequency weight being provided by the transfer function matrix G_(I).The process performed in the current controller 74″ is expressed as thetransfer function matrix G′_(I), and therefore is a lineartime-invariant process. Hence, it is possible to perform control systemdesign using a linear control theory. It should be noted here that alinear control method other than the H∞ loop shaping method may beutilized in the design.

In the present embodiment, the current controller 74″ which performs theprocess represented by the transfer function matrix G′_(I) performs aprocess equivalent to the PI control in FIG. 37 performed by thethree-phase to two-phase converter 73, the two-phase to three-phaseconverter 76, the fixed-to-rotating coordinate converter 78, therotating-to-fixed coordinate converter 79, and the I control(implemented by the PI control performed by the PI controller 74 b andthe PI controller 75 b in FIG. 37). Also, the process performed in thecurrent controller 74″ is expressed as the transfer function matrixG′_(I), and therefore is a linear time-invariant process. Therefore, theentire current control system is a linear time-invariant system, andhence, the arrangement enables control system design and system analysisusing a linear control theory.

If negative phase sequence component control of the fundamental wavecomponent is to be performed in the third embodiment, it can be achievedby using a transfer function matrix G′_(I) in which the elementsG_(I12)(s), G_(I23)(s), G_(I31)(s) are swapped with the elementsG_(I13)(s), G_(I21)(s) and G_(I32)(s) respectively (in other words, atransposed matrix of the matrix G_(I) should be used).

Next, description will cover a case where both of the positive-phase andthe negative-phase sequence components in the fundamental wave componentare controlled in the third embodiment.

If “0” is given to the element (1, 2) and the element (2, 1) of thematrix G in the Equation (14) described above, the calculation providesa transfer function matrix G″ represented by Equation (17) shown below.

$\begin{matrix}\begin{matrix}{G^{''} = {{{\frac{2}{3}\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}\begin{bmatrix}\frac{\begin{matrix}{{F\left( {s + {j\; \omega_{0}}} \right)} +} \\{F\left( {s - {j\; \omega_{0}}} \right)}\end{matrix}}{2} & 0 \\0 & \frac{\begin{matrix}{{F\left( {s + {j\; \omega_{0}}} \right)} +} \\{F\left( {s - {j\; \omega_{0}}} \right)}\end{matrix}}{2}\end{bmatrix}} \times}} \\{\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}} \\{= {\frac{1}{3} \cdot {\frac{{F\left( {{s \cdot j}\; \omega_{0}} \right)} + {F\left( {S - {j\; \omega_{0}}} \right)}}{2}\begin{bmatrix}2 & {- 1} & {- 1} \\{- 1} & 2 & {- 1} \\{- 1} & {- 1} & 2\end{bmatrix}}}}\end{matrix} & (17)\end{matrix}$

Therefore, a transfer function matrix G″_(I) which represents theprocess performed by the current controller 74″ when controlling both ofthe positive-phase and the negative phase sequence components areexpressed by Equation (18) shown below:

$\begin{matrix}{G_{1}^{''} = {\frac{1}{3} \cdot {\frac{K_{I}s}{s^{2} + \omega_{0}^{2}}\begin{bmatrix}2 & {- 1} & {- 1} \\{- 1} & 2 & {- 1} \\{- 1} & {- 1} & 2\end{bmatrix}}}} & (18)\end{matrix}$

Thus far, in the first through the third embodiments, description wasmade for cases where the current controller 74 (the alpha axis currentcontroller 74′, the beta axis current controller 75′, the currentcontroller 74″) performs a control which replaces the I control.However, the present invention is not limited by these. For example, analternative control which replaces the PI control may be provided. Ifthe current controller 74 in the first embodiment is to perform acontrol which replaces the PI control, it can be achieved by using atransfer function matrix G_(PI) represented by Equation (11) above.

FIG. 12 is a Bode diagram for analyzing transfer functions as elementsof a matrix G_(PI). FIG. 12( a) shows transfer functions of the element(1, 1) and the element (2, 2) of the matrix G_(PI) whereas FIG. 12 (b)shows a transfer function of the element (1, 2) of the matrix G_(PI),and FIG. 12( c) shows a transfer function of the element (2, 1) of thematrix G_(PI). FIG. 12 shows a case where the center frequency is 60 Hz,an integral gain K_(I) is fixed to 1 and the proportional gain K_(P) isset to “0.1”, “1”, “10” and “100”.

FIG. 12( a) shows an amplitude characteristic which has a peak at thecenter frequency. As the proportional gain K_(P) increases, theamplitude characteristic increases except at the center frequency. Thephase characteristic comes to zero degree at the center frequency. Inother words, the transfer functions for the element (1, 1) and theelement (2, 2) of the matrix G_(I) allow signals of the center frequency(center angular frequency) to pass through without changing the phase.

Amplitude characteristics in FIG. 12( b) and FIG. 12( c) also have theirpeaks at the center frequency. The amplitude characteristics and thephase characteristics are constant regardless of the proportional gainK_(P). Also, the phase characteristic in FIG. 12( b) attains 90 degreesat the center frequency. In other words, the transfer function of theelement (1, 2) of the matrix G_(PI) allows signals of the centerfrequency (center angular frequency) to pass through with a 90-degreephase advance. On the other hand, the phase characteristic in FIG. 12(c) attains −90 degrees at the center frequency. In other words, thetransfer function of the element (2, 1) of the matrix G_(I) allowssignals of the center frequency (center angular frequency) to passthrough with a 90-degree phase delay.

If the alpha axis current controller 74′ and the beta axis currentcontroller 75′ in the second embodiment are to perform an alternativecontrol which replaces the PI control, it can be achieved by using atransfer function (K_(P)·s²+K_(I)·s+K_(P)·ω₀ ²)/(s²+ω₀ ²) whichrepresents the element (1, 1) and the element (2, 2) in the transferfunction matrix G_(PI) represented by Equation (11) above.

If the current controller 74″ in the third embodiment is to perform analternative control which replaces the PI control, it can be achieved byusing a transfer function matrix G′_(PI) represented by Equation (19)shown below:

$\begin{matrix}{{G_{PI}^{\prime} = \begin{bmatrix}{G_{{PI}\; 11}(s)} & {G_{{PI}\; 12}(s)} & {G_{{PI}\; 13}(s)} \\{G_{{PI}\; 21}(s)} & {G_{{PI}\; 22}(s)} & {G_{{PI}\; 23}(s)} \\{G_{{PI}\; 31}(s)} & {G_{{PI}\; 32}(s)} & {G_{{PI}\; 33}(s)}\end{bmatrix}}{{where}\text{:}}\begin{matrix}{{G_{{PI}\; 11}(s)} = {G_{{PI}\; 22}(s)}} \\{= {G_{{PI}\; 33}(s)}} \\{= {\frac{1}{3}\left( {K_{p} + \frac{K_{I}}{s + {j\; \omega_{0}}} + K_{P} + \frac{K_{I}}{s - {j\; \omega_{0}}}} \right)}} \\{= {\frac{2}{3} \cdot \frac{{K_{P}s^{2}} + {K_{I}s} + {K_{P}\omega_{0}^{2}}}{s^{2} + \omega_{0}^{2}}}}\end{matrix}\begin{matrix}{{G_{{PI}\; 12}(s)} = {G_{{PI}\; 23}(s)}} \\{= {G_{{GI}\; 31}(s)}} \\{= {\frac{1}{6}\begin{Bmatrix}{{\left( {{- 1} - {\sqrt{3}j}} \right) \cdot \left( {K_{P} + \frac{K_{I}}{s + {j\; \omega_{0}}}} \right)} +} \\{\left( {{- 1} + {\sqrt{3}j}} \right){\cdot \left( {K_{P} + \frac{K_{I}}{s - {j\; \omega_{0}}}} \right)}}\end{Bmatrix}}} \\{= {{- \frac{1}{3}} \cdot \frac{{K_{P}s^{2}} + {K_{I}\left( {s + {\sqrt{3}\omega_{0}}} \right)} + {K_{P}\omega_{0}^{2}}}{s^{2} + \omega_{0}^{2}}}}\end{matrix}\begin{matrix}{{G_{{PI}\; 13}(s)} = {G_{{PI}\; 21}(s)}} \\{= {G_{{GI}\; 32}(s)}} \\{= {\frac{1}{6}\begin{Bmatrix}{{\left( {{- 1} + {\sqrt{3}j}} \right) \cdot \left( {K_{P} + \frac{K_{I}}{s + {j\; \omega_{0}}}} \right)} +} \\{\left( {{- 1} - {\sqrt{3}j}} \right){\cdot \left( {K_{P} + \frac{K_{I}}{s - {j\; \omega_{0}}}} \right)}}\end{Bmatrix}}} \\{= {{- \frac{1}{3}} \cdot \frac{{K_{P}s^{2}} + {K_{I}\left( {s + {\sqrt{3}\omega_{0}}} \right)} + {K_{P}\omega_{0}^{2}}}{s^{2} + \omega_{0}^{2}}}}\end{matrix}} & (19)\end{matrix}$

Also, if the current controller 74″ is to perform an alternative controlwhich replaces the PI control in an arrangement where both of thepositive-phase and the negative-phase sequence components are controlledin the third embodiment, it can be achieved by using a transfer functionmatrix G″_(PI) represented by Equation (20) shown below:

$\begin{matrix}{G_{PI}^{''} = {\frac{1}{3} \cdot {\frac{{K_{P}s^{2}} + {K_{I}s} + {K_{P}\omega_{0}^{2}}}{s^{2} + \omega_{0}^{2}}\begin{bmatrix}2 & {- 1} & {- 1} \\{- 1} & 2 & {- 1} \\{- 1} & {- 1} & 2\end{bmatrix}}}} & (20)\end{matrix}$

Providing alternative control which replaces the PI control offers anadvantage that a damping effect can be added at transient time byadjusting the proportional gain K_(P). However, there is also adisadvantage that the system is more sensitive to modeling errors. Onthe contrary, providing control which replaces the I control isdisadvantageous in that a damping effect at transient time cannot beadded, yet there is an advantage that the system is not very muchsensitive to modeling errors.

It should be noted here that there may be an arrangement that thecurrent controller 74 (the alpha axis current controller 74′, the betaaxis current controller 75′, the current controller 74″) provides analternative control which replaces the above-described alternativecontrols to I control or PI control. If the transfer function F(s) inEquation (10) is substituted for a transfer function of the intendedcontrol, the equation provides a transfer function matrix whichrepresents a process equivalent to carrying out fixed-to-rotatingcoordinate conversion, the intended control and then rotating-to-fixedcoordinate conversion. Therefore, it is possible to design a systemwhich provides an alternative control (the transfer function for whichis expressed as F(s)=K_(P)+K_(I)/s+K_(D)·s, where K_(P) is proportionalgain, K_(I) is integral gain, and K_(D) is derivative gain) whichreplaces the PID control. It is also possible to provide control whichcan replace D control (derivative control: the transfer function forwhich is expressed by F(s)=K_(D)·s, where K_(D) is derivative gain); Pcontrol (proportional control: the transfer function for which isexpressed by F(s)=K_(P), where K_(P) is proportional gain), PD control,ID control, etc.

In the first through the third embodiments thus far, description wasmade for cases where output current was controlled. However, the presentinvention is not limited to this. For example, output voltage may becontrolled. Hereinafter, a case of controlling the output voltage willbe described as a fourth embodiment.

FIG. 13 is a block diagram for describing a control circuit according tothe fourth embodiment. In this figure, elements which are identical withor similar to those in the interconnection inverter system A in FIG. 6are indicated by the same reference codes.

An inverter system A′ in FIG. 13 differs from the interconnectioninverter system A (see FIG. 6) according to the first embodiment in thatthe system supplies power to a load L instead of the electrical powersystem B. Since it is necessary to control the voltage which is suppliedto the load L, a control circuit 8 controls the output voltage, insteadof the output current. The control circuit 8 differs from the controlcircuit 7 (see FIG. 6) according to the first embodiment in that itgenerates PWM signals based on voltage signals V from the voltage sensor6. The inverter system A′ supplies power to the Load L while controllingthe output voltage at a target value through feedback control.

A three-phase to two-phase converter 83 receives three voltage signalsVu, Vv, Vw from the voltage sensor 6 and converts these voltage signalsinto an alpha axis voltage signal Vα and a beta axis voltage signal Vβ.The conversion process performed in the three-phase to two-phaseconverter 83 is represented by a formula shown below as Equation (21).

$\begin{matrix}{\begin{bmatrix}{V\; \alpha} \\{V\; \beta}\end{bmatrix} = {{\sqrt{\frac{2}{3}}\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}\begin{bmatrix}{Vu} \\{Vv} \\{Vw}\end{bmatrix}}} & (21)\end{matrix}$

The voltage signals Vu, Vv, Vw are phase voltage signals in respectivephases. Alternatively however, line voltage signals may be detected andused. In this case, the line voltage signals may be converted into phasevoltage signals and then the formula represented by Equation (21) aboveis utilized. Another option may be to use a matrix, in place of the onerepresented by Equation (21), which converts the line voltage signalsinto an alpha axis voltage signal Vα and a beta axis voltage signal Vβ.

A voltage controller 84 receives deviations of the alpha axis voltagesignal Iα and the beta axis voltage signal Iβ outputted by thethree-phase to two-phase converter 83 from their respective targetvalues, to generate correction value signals Xα, Xβ for the voltagecontrol. A voltage controller 84 performs a process represented by thetransfer function matrix G_(I) represented by Equation (12). In otherwords, the controller performs a process given by Equation (22) belowwhere the deviations of the alpha axis voltage signal Iα and of the betaaxis voltage signal Iβ from their respective target values arerepresented by ΔVα and ΔVβ. As for the angular frequency ω₀, apredetermined value is set as an angular frequency (for example, ω₀=120π[rad/sec] (60 [Hz])) for the system voltage fundamental wave, and theintegral gain K_(I) is a pre-designed value. Also, the voltagecontroller 84 performs a stability margin maximization process, whichincludes phase adjustment to correct phase delay in the control loop.The deviations ΔVα, ΔVβ represent “the first input signal” and “thesecond input signal” respectively according to the present inventionwhereas the correction value signals Xα, Xβ represent “the first outputsignal” and “the second output signal” respectively according to thepresent invention.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{X\; \alpha} \\{X\; \beta}\end{bmatrix} = {G_{I}\begin{bmatrix}{\Delta \; V\; \alpha} \\{\Delta \; V\; \beta}\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{K_{I}s}{s^{2} + \omega_{0}^{2}} & \frac{{- K_{I}}\omega_{0}}{s^{2} + \omega_{0}^{2}} \\\frac{K_{I}\omega_{0}}{s^{2} + \omega_{0}^{2}} & \frac{K_{I}s}{s^{2} + \omega_{0}^{2}}\end{bmatrix}\begin{bmatrix}{\Delta \; V\; \alpha} \\{\Delta \; V\; \beta}\end{bmatrix}}}\end{matrix} & (22)\end{matrix}$

In the present embodiment, the alpha axis voltage target value and thebeta axis voltage target value are provided by values obtained byrotating-to-fixed coordinate conversion of the d axis voltage targetvalue and the q axis voltage target value respectively. It should benoted here that in cases where three-phase voltage target values aregiven, those target values should be subjected to three-phase totwo-phase conversion to obtain the alpha axis voltage target value andthe beta axis voltage target value. Also, if the alpha axis voltagetarget value and the beta axis voltage target value are supplieddirectly, the supplied target values may be used directly.

In the present embodiment, the voltage controller 84 is designed by H∞loop shaping method, which is based on a linear control theory, with afrequency weight being provided by the transfer function matrix G_(I).The process performed in the voltage controller 84 is expressed by thetransfer function matrix G_(I), and therefore is a linear time-invariantprocess. Hence, it is possible to perform control system design using alinear control theory. It should be noted here that a linear controlmethod other than the H∞ loop shaping method may be utilized in thedesign.

In the present embodiment, the control circuit 8 performs control in thefixed coordinate system without making fixed-to-rotating coordinateconversion nor rotating-to-fixed coordinate conversion. As has beendescribed earlier, the transfer function matrix G_(I) is a transferfunction matrix which represents an equivalent process to carrying outfixed-to-rotating coordinate conversion, then I control and thenrotating-to-fixed coordinate conversion. Therefore, the voltagecontroller 84 which performs the process represented by the transferfunction matrix G_(I) performs an equivalent process to the processperformed by the fixed-to-rotating coordinate converter 78, therotating-to-fixed coordinate converter 79, and I control process in FIG.37. Also, as shown in each Bode diagram in FIG. 7, the transfer functionfor each element in the matrix G_(I) has an amplitude characteristicwhich attains its peak at the center frequency. In other words, in thevoltage controller 84, only the center frequency component is ahigh-gain component. Therefore, there is no need for providing the LPF74 a or 75 a in FIG. 37.

The process performed in the voltage controller 84 is expressed by thetransfer function matrix G_(I), and therefore is a linear time-invariantprocess. Also, the control circuit 8 does not include nonlineartime-varying processes, i.e., the circuit does not includefixed-to-rotating coordinate conversion process nor rotating-to-fixedcoordinate conversion process. Hence, the entire voltage control systemis a linear time-invariant system. Therefore, the arrangement enablescontrol system design and system analysis using a linear control theory.As described, use of the transfer function matrix G_(I) represented byEquation (12) enables to replace the non-linear process in whichfixed-to-rotating coordinate conversion is followed by I control andthen by rotating-to-fixed coordinate conversion with a lineartime-invariant multi-input multi-output system. This makes it easy toperform system analysis and control system design.

It should be noted here that in the present embodiment, the voltagecontroller 84 performs the process represented by Equation (22).However, each element in the matrix G_(I) may be given a different valuefrom others for its integral gain K_(I). Specifically, an integral gainK_(I) which differ from one transfer function to another may be designedfor each element. For example, there may be a design to includeadditional characteristics in the alpha axis component such as improvedquick response, improved stability, etc. Another example of giving anadditional characteristic may be to assign “0” to the integral gainK_(I) of the element (1, 2) and that of the element (2, 1), to controlboth of negative-phase and negative-phase sequence components. Also, ifnegative phase sequence component control is to be performed, it can beaccomplished by using the transfer function matrix G_(I) in which theelement (1, 2) and the element (2, 1) are swapped with each other.

Also, if positive phase sequence component is to be controlled using thethree voltage signals Vu, Vv, Vw, it can be achieved by using thetransfer function matrix G′_(I). If negative phase sequence componentsare to be controlled, it can be achieved by using the transfer functionmatrix G′_(I) in which the elements G_(I12)(s), G_(I23)(s), G_(I31)(s)are swapped with G_(I13)(s), G_(I21)(s), G_(I32)(s) (i.e., a transposedmatrix of the matrix G′_(I) should be used). If both of thepositive-phase and the negative-phase sequence components are to becontrolled, it can be accomplished by using the transfer function matrixG″_(I) represented by Equation (18). Also, there may be arrangementswhere the voltage controller 84 does not provide the alternative controlwhich replaces the I control, but provides a different alternativecontrol (such as PI control, D control, P control, PD control, IDcontrol, and PID control) which replaces the above-described alternativecontrols.

Next, description will cover a case where switching is made betweenoutput voltage control and output current control, as a fifthembodiment.

In normal situations, an interconnection inverter system supplieselectric power to an electrical power system while controlling itsoutput in association with the electrical power system. If there is anaccident in the electrical power system, the inverter circuit willdisconnect itself from the electrical power system and then ceases itsoperation. However, there is an increasing demand for interconnectioninverter systems which operate autonomously during an accident in theelectrical power system for continued supply of power to a load which isconnected to the interconnection inverter system. If an interconnectioninverter system is to perform autonomous operation to supply power to aload, it is necessary to control output voltage. An interconnectioninverter system according to the fifth embodiment is such a system whichis implemented by a combination of the first embodiment and the fourthembodiment and is capable of switching its operation between outputvoltage control and output current control.

FIG. 14 is a block diagram for describing a control circuit according tothe fifth embodiment. In this figure, elements which are identical withor similar to those in the interconnection inverter system A in FIG. 6are indicated by the same reference codes.

FIG. 14 shows an interconnection inverter system A″, which suppliespower to a load L while also supplying power to the electrical powersystem B if it is interconnected therewith. It should be noted here thatthe interconnection inverter system A according to the first embodimentworks in the same manner. However, description for the first embodimentonly covered a situation where the system was interconnected with theelectrical power system B, and therefore no reference or description wasmade for the load L. The interconnection inverter system A″ performscurrent control when it is in connection with the electrical powersystem B but performs voltage control when it is disconnected from theelectrical power system B.

FIG. 14 shows a control circuit 8″, which differs from the controlcircuit 7 (see FIG. 6) according to the first embodiment in that itincludes a three-phase to two-phase converter 83, a voltage controller84, a two-phase to three-phase converter 76 and a PWM signal generator77 for voltage control, and a control switcher 85.

The three-phase to two-phase converter 83 and the voltage controller 84are identical with the three-phase to two-phase converter 83 and thevoltage controller 84 (see FIG. 13) according to the fourth embodiment.In other words, they generate correction value signals Xα, Xβ based onthree voltage signals Vu, Vv, Vw from the voltage sensor 6. Then, thetwo-phase to three-phase converter 76 and the PWM signal generator 77 inthe subsequent stages generate PWM signals for the voltage control. Onthe other hand, the three-phase to two-phase converter 73 and thecurrent controller 74 generate correction value signals Xα, Xβ based onthree current signals Iu, Iv, Iw from the current sensor 5. Then, thetwo-phase to three-phase converter 76, the system matching-fractiongenerator 72 and the PWM signal generator 77 in the subsequent stagesgenerate PWM signals for the voltage control. The control switcher 85outputs PWM signals for voltage control generated by the voltagecontroller 84 based on the correction value signals Xα, Xβ when notconnected with the electrical power system B, while it outputs the PWMsignals for current control generated by the current controller 74 basedon the correction value signals Xα, Xβ when connected with theelectrical power system B.

In the present embodiment, the interconnection inverter system A″ iscapable of performing current control thereby supplying power to theelectrical power system B when it is connected with the electrical powersystem B whereas it is capable of performing voltage control therebysupplying power to the load L when not connected with the electricalpower system B. Also, in the present embodiment, the control circuit 8′performs control in the fixed coordinate system without makingfixed-to-rotating coordinate conversion nor rotating-to-fixed coordinateconversion. Since the processes performed in the current controller 74and the voltage controller 84 are processes which are equivalent to aprocess in which fixed-to-rotating coordinate conversion is followed byI control and then by rotating-to-fixed coordinate conversion, and areexpressed by a transfer function matrix G_(I), they are lineartime-invariant processes. Therefore, each of the entire current controlsystem and the entire voltage control system is a linear time-invariantsystem, and hence, the arrangement enables control system design andsystem analysis using a linear control theory.

In the first through the fifth embodiments, description was made forcases where the control circuit according to the present invention wasapplied to an interconnection inverter system (inverter system).However, the present invention is not limited to this. The presentinvention is also applicable to control circuits which control invertercircuits used in unbalance compensators, static reactive powercompensators (SVC, SVG), power active filters, uninterruptable powersupply systems (UPS), and so on. The present invention is alsoapplicable to control circuits for controlling inverter circuits whichcontrol rotation of motors or of electric power generators Further, thepresent invention is not limited to controlling those inverter circuitswhich convert DC current into three-phase AC current. For example, theinvention is applicable to control circuits for converters which convertthree-phase AC current into DC current and for cyclo-converters whichconvert three-phase AC frequencies. Hereinafter, description will covera case where the present invention is applied to a control circuit of aconverter circuit, as a sixth embodiment.

FIG. 15 is a block diagram for describing a three-phase PWM convertersystem according to the sixth embodiment. In this figure, elements whichare identical with or similar to those in the interconnection invertersystem A in FIG. 6 are indicated by the same reference codes.

FIG. 15 shows a three-phase PWM converter system C which converts ACpower from an electrical power system B into DC power and supplies theDC power to a load L′. The load L′ is a DC load. The three-phase PWMconverter system C includes a voltage transformer circuit 4, a filtercircuit 3, a current sensor 5, a voltage sensor 6, a converter circuit2′, and a control circuit 7.

The voltage transformer circuit 4 increases or decreases the AC voltagefrom the electrical power system B to a predetermined level. The filtercircuit 3 removes high frequency components from the AC voltage inputtedfrom the voltage transformer circuit 4, and outputs the filtered voltageto the converter circuit 2′. The current sensor 5 detects an AC currentof each phase inputted to the converter circuit 2′. The detected currentsignals I are inputted to the control circuit 7. The voltage sensor 6detects an AC voltage of each phase inputted to the converter circuit2′. The detected voltage signals V are inputted to the control circuit7. The converter circuit 2′ converts the inputted AC voltages into a DCvoltage and output the DC voltage to the load L′. The converter circuit2′ is a three-phase PWM converter, i.e., a voltage-type convertercircuit which includes unillustrated six switching elements in threesets. The converter circuit 2′ switches ON and OFF each of the switchingelements based on PWM signals from the control circuit 7, therebyconverting the inputted AC voltages to a DC voltage. The convertercircuit 2′ is not limited to this, and may be provided by a current-typeconverter circuit.

The control circuit 7 controls the converter circuit 2′. Like thecontrol circuit 7 according to the first embodiment, the control circuit7 generates PWM signals and outputs the generated signals to theconverter circuit 2′. FIG. 15 only shows a configuration for inputcurrent control. The figure does not show other control configurations.Though not illustrated, the control circuit 7 also includes a DC voltagecontroller and a reactive power controller thereby providing control onoutput voltage and input reactive power. The type of control performedby the control circuit 7 is not limited to the above. For example, ifthe converter circuit 2′ is a current-type converter circuit, outputcurrent control is performed instead of the output voltage control.

The present embodiment provides the same advantages as offered by thefirst embodiment. If the three-phase PWM converter system C is to bereduced in its size by reducing the size of the filter circuit 3,accuracy in current control will have to be decreased, which leads toincreased difficulty in control system design. However, according to thepresent embodiment, system design can be easy by using a linear controltheory. Therefore, difficulty in control system design is no longer ahurdle to size reduction of the three-phase PWM converter system C.

The configuration of the three-phase PWM converter system C is notlimited to the above. For example, the control circuit 7 may be replacedby the control circuit 7′, 7″, 8 or 8′. Also, an inverter circuit may beprovided on the output side of the converter circuit 2′ for conversionof the DC power further into AC power for supply to an AC load. In thiscase the system provides a cyclo-converter.

Next, methods of controlling harmonic components will be described.

The transfer function matrix G represented by Equation (10) is forcontrolling a fundamental wave component. The n-th harmonic is anangular frequency component obtained by multiplying the fundamental waveangular frequency by n. When the n-th-order harmonic positive phasesequence component is subjected to three-phase to two-phase conversion,two cases are possible: In one case the alpha axis signal has anadvanced phase over the beta axis signal, and in the other case thephase is delayed. If n=3k+1 (k=1, 2, . . . ), the n-th-order harmonicpositive phase sequence component signal has a sequence of phases whichis identical with that in the positive phase sequence component signalof the fundamental wave. Specifically, with the fundamental wave'spositive phase sequence component having U-, V-, and W-phase signalsrepresented by Vu=V cos θ, Vv=V cos(θ−2π/3) and Vw=V cos(θ−4π/3)respectively, signals of e.g. the seventh-order harmonic positive phasesequence component in the U, V and W phases are expressed as Vu₇=V₇ cos7θ, Vv₇=V₇ cos(7θ−14π/3)=V cos(7θ−2π/3), and Vw₇=V₇ cos(7θ−28π/3)=V₇cos(7θ−4π/3) respectively. In this case, the phase sequence is identicalwith that of the positive phase sequence component in the fundamentalwave, and like in FIG. 8( a), the phase of the alpha axis signal isadvanced by 90 degrees over the phase of the beta axis signal.Therefore, the transfer function matrix to control positive phasesequence component of the n-th-order harmonic (n=3k+1) is expressed as atransfer function matrix G_(n) represented by Equation (23) which isEquation (10) with the item ω₀ substituted for n·ω₀. On the other hand,if n=3k+2 (k=1, 2, . . . ), the n-th-order harmonic positive phasesequence component signal has a phase sequence which is identical withthat of the negative phase sequence component signal of the fundamentalwave. Specifically, with the fundamental wave's positive phase sequencecomponent having U-, V-, and W-phase signals Vu, Vv, Vw beingrepresented by the same equations as the above, signals of e.g. thefifth-order harmonic positive phase sequence components in the U, V andW phases are expressed as, Vu₅=V₅ cos 5θ, Vv₅=V₅ cos(5θ−10π/3)=V₅cos(5θ−4π/3), and Vw₅=V₅ cos(5θ−20π/3)=V₅ cos(5θ−2π/3) respectively. Inthis case, the phase sequence is identical with that of the negativephase sequence component in the fundamental wave, and like in FIG. 8(b), the phase of the alpha axis signal is delayed by 90 degrees from thephase of the beta axis signal. Therefore, the transfer function matrixto control the positive phase sequence component of the n-th-orderharmonic (n=3k+2) is expressed as a transfer function matrix G_(n)represented by Equation (23′) which is Equation (10) in which the itemω₀ is substituted for n·ω₀ and the elements (1, 2) and the element (2,1) are swapped with each other.

$\begin{matrix}{{Gn} = \begin{bmatrix}\frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2} & \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} - {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2\; j} \\{- \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} - {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2\; j}} & \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2}\end{bmatrix}} & (23) \\{{Gn} = \begin{bmatrix}\frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2} & {- \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} - {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2\; j}} \\\frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} - {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2\; j} & \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2}\end{bmatrix}} & \left( 23^{\prime} \right)\end{matrix}$

Also, the transfer function matrix G_(In) to perform I control on thepositive phase sequence component of the n-th-order harmonic (n=3k+1) iscalculated as Equation (24) which is Equation (12) in which the item ω₀is substituted for n·ω₀. On the other hand, the matrix G_(In) of thetransfer function to provided I control on the positive phase sequencecomponent of the n-th-order harmonic (n=3k+2) is calculated as Equation(24′) which is Equation (12) in which the item ω₀ is substituted forn·ω₀ and the element (1, 2) and the element (2, 1) are swapped with eachother. The following Equations (24) and (24′) can be obtained asF(s)=K_(I)/s in Equations (23) and (23′).

$\begin{matrix}{G_{In} = \begin{bmatrix}\frac{K_{I}s}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{{- K_{I}}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} \\\frac{K_{I}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{K_{I}s}{s^{2} + {n^{2}\omega_{0}^{2}}}\end{bmatrix}} & (24) \\{G_{In} = \begin{bmatrix}\frac{K_{I}s}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{K_{I}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} \\\frac{{- K_{I}}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{K_{I}s}{s^{2} + {n^{2}\omega_{0}^{2}}}\end{bmatrix}} & \left( 24^{\prime} \right)\end{matrix}$

Hereinafter, description will be made for a seventh embodiment of thepresent invention, which is a case where a harmonic compensationcontroller which performs the process given by the transfer functionmatrix G_(In) in Equations (24) and (24′) is applied to aninterconnection inverter system control circuit.

FIG. 16 is a block diagram for describing the interconnection invertersystem according to the seventh embodiment. In this figure, elementswhich are identical with or similar to those in the control circuit 7 inFIG. 6 are indicated by the same reference codes. FIG. 16 shows acontrol circuit 7, which is the control circuit 7 (see FIG. 6) accordingto the first embodiment further including a harmonic compensationcontroller 9.

The harmonic compensation controller 9 works for harmonic componentsuppression. It receives an alpha axis current signal Iα and a beta axiscurrent signal Iβ from the three-phase to two-phase converter 73, andgenerates harmonic compensation signals Yα, Yβ for harmonic suppressioncontrol. The harmonic compensation controller 9 includes a fifth-orderharmonic compensator 91 for suppressing positive phase sequencecomponent of the fifth-order harmonic; a seventh-order harmoniccompensator 92 for suppressing positive phase sequence component of theseventh-order harmonic; and an eleventh-order harmonic compensator 93for suppressing positive phase sequence component of the eleventh-orderharmonic.

The fifth-order harmonic compensator 91 works for suppressing positivephase sequence component of the fifth-order harmonic. The fifth-orderharmonic compensator 91 performs a process given by a transfer functionmatrix G_(I5), which is the transfer function matrix Gin represented byEquation (24′) with n=5 for the control of positive phase sequencecomponent of the fifth-order harmonic. In other words, the fifth-orderharmonic compensator 91 performs a process given by the followingEquation (25), to output fifth-order harmonic compensation signals Yα₅,Yβ₅. As for the angular frequency ω₀, a predetermined value is set as anangular frequency (for example, ω₀=120π [rad/sec] (60 [Hz])) for thesystem voltage fundamental wave, and the integral gain K_(I5) is apre-designed value. Also, the fifth-order harmonic compensator 91performs a stability margin maximization process, which includes phaseadjustment to correct phase delay in the control loop for reversing thephase. The alpha axis current signal Iα and the beta axis current signalIβ represent “the first input signal” and “the second input signal”according to the present invention respectively whereas the fifth-orderharmonic compensation signals Yα₅, Yβ₅ represent “the first outputsignal” and “the second output signal” according to the presentinvention respectively.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{Y\; \alpha_{5}} \\{Y\; \beta_{5}}\end{bmatrix} = {G_{I\; 5}\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{K_{I\; 5}s}{s^{2} + {25\omega_{0}^{2}}} & \frac{K_{I\; 5}n\; \omega_{0}}{s^{2} + {25\omega_{0}^{2}}} \\\frac{{- 5}K_{I\; 5}\omega_{0}}{s^{2} + {25\omega_{0}^{2}}} & \frac{K_{I\; 5}s}{s^{2} + {25\omega_{0}^{2}}}\end{bmatrix}\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix}}}\end{matrix} & (25)\end{matrix}$

In the present embodiment, the fifth-order harmonic compensator 91 isdesigned by H∞ loop shaping method, which is a method based on a linearcontrol theory, with a frequency weight being provided by the transferfunction matrix G_(I5). The process performed in the fifth-orderharmonic compensator 91 is expressed as the matrix G_(I5) of thetransfer function, and therefore is a linear time-invariant process.Hence, it is possible to perform control system design using a linearcontrol theory.

It should be noted here that design method to be used in designing thecontrol system is not limited to this. In other words, other linearcontrol theories may be employed for the design. Examples of usablemethods include loop shaping method, optimum control, H∞ control, mixedsensitivity problem, and more. Also, there may be an arrangement that aphase θ₅ is calculated and set in advance for adjustment based on thephase delay. For example, if the target of control has a 90-degree phasedelay, a 180-degree phase delay may be designed by a setting θ₅=−90degrees. In this case, a rotation conversion matrix based on the phaseθ₅ is added to Equation (25).

The seventh-order harmonic compensator 92 works for suppressing positivephase sequence component of the seventh-order harmonic. Theseventh-order harmonic compensator 92 performs a process given by atransfer function matrix G_(I7), which is the transfer function matrixG_(In) represented by Equation (24) with n=7 for the control of positivephase sequence component of the seventh-order harmonics. In other words,the seventh-order harmonic compensator 92 performs a process given bythe following Equation (26), to output seventh-order harmoniccompensation signals Yα₇, Yβ₇. As for the angular frequency ω₀, apredetermined value is set as an angular frequency for the systemvoltage fundamental wave, and the integral gain K_(I7) is a pre-designedvalue. Also, the seventh-order harmonic compensator 92 performs astability margin maximization process, which includes phase adjustmentto correct phase delay in the control loop for reversing the phase. Theseventh-order harmonic compensator 92 is designed by the same method asis the fifth-order harmonic compensator 91.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{Y\; \alpha_{7}} \\{Y\; \beta_{7}}\end{bmatrix} = {G_{I\; 7}\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{K_{I\; 7}s}{s^{2} + {49\omega_{0}^{2}}} & \frac{{- 7}K_{I\; 7}n\; \omega_{0}}{s^{2} + {49\omega_{0}^{2}}} \\\frac{7K_{I\; 7}\omega_{0}}{s^{2} + {49\omega_{0}^{2}}} & \frac{K_{I\; 7}s}{s^{2} + {49\omega_{0}^{2}}}\end{bmatrix}\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix}}}\end{matrix} & (26)\end{matrix}$

The eleventh-order harmonic compensator 93 works for suppressingpositive phase sequence component of the eleventh-order harmonics. Theeleventh-order harmonic compensator 93 performs a process given by atransfer function matrix G_(I11), which is the transfer function matrixG_(In) represented by Equation (24′) with n=11 for the control ofpositive phase sequence component of the eleventh-order harmonics. Inother words, the eleventh-order harmonic compensator 93 performs aprocess given by the following Equation (27), to output eleventh-orderharmonic compensation signals Yα11, Yβ11. As for the angular frequencyω₀, a predetermined value is set as an angular frequency for the systemvoltage fundamental wave, and the integral gain K_(I11) is apre-designed value. Also, the eleventh-order harmonic compensator 93performs a stability margin maximization process, which includes phaseadjustment to correct phase delay in the control loop for reversing thephase. The eleventh-order harmonic compensator 93 is designed by thesame method as is the fifth-order harmonic compensator 91.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{Y\; \alpha_{11}} \\{Y\; \beta_{11}}\end{bmatrix} = {G_{I\; 11}\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{K_{I\; 11}s}{s^{2} + {121\omega_{0}^{2}}} & \frac{11K_{I\; 11}\omega_{0}}{s^{2} + {121\omega_{0}^{2}}} \\\frac{{- 11}K_{I\; 11}\omega_{0}}{s^{2} + {121\omega_{0}^{2}}} & \frac{K_{I\; 11}s}{s^{2} + {121\omega_{0}^{2}}}\end{bmatrix}\begin{bmatrix}{I\; \alpha} \\{I\; \beta}\end{bmatrix}}}\end{matrix} & (27)\end{matrix}$

The fifth-order harmonic compensation signals Yα₅, Yβ₅ outputted by thefifth-order harmonic compensator 91, the seventh-order harmoniccompensation signals Yα₇, Yβ₇ outputted by the seventh-order harmoniccompensator 92, and the eleventh-order harmonic compensation signalsYα₁₁, Yβ₁₁ outputted by the eleventh-order harmonic compensator 93 areadded together respectively, and the resulting harmonic compensationsignals Yα, Yβ are outputted from the harmonic compensation controller9. It should be noted here that the present embodiment covers a casewhere the harmonic compensation controller 9 includes the fifth-orderharmonic compensator 91, the seventh-order harmonic compensator 92, andthe eleventh-order harmonic compensator 93. However, the presentinvention is not limited to this. The harmonic compensation controller 9is designed in accordance with the orders of harmonics which must besuppressed. For example, if the fifth-order harmonics are the onlytarget of suppression, then only the fifth-order harmonic compensator 91may be included. Likewise, if it is desired to suppress thethirteenth-order harmonic, then a thirteenth-order harmonic compensatorshould be added for a process expressed by a matrix G_(I13), which isthe transfer function matrix G_(In) with n=13 represented by Equation(24).

The harmonic compensation signals Yα, Yβ outputted from the harmoniccompensation controller 9 are added to the correction value signals Xα,Xβ outputted from the current controller 74. The two-phase tothree-phase converter 76 is fed with correction value signals Xα, Xβobtained by the addition of the harmonic compensation signals Yα, Yβ.

In the present embodiment, the fifth-order harmonic compensator 91performs control in the fixed coordinate system without makingfixed-to-rotating coordinate conversion nor rotating-to-fixed coordinateconversion. The matrix G_(I5) of the transfer function is a transferfunction matrix which shows a process equivalent to carrying outfixed-to-rotating coordinate conversion, then I control and thenrotating-to-fixed coordinate conversion.

Also, the process performed in the fifth-order harmonic compensator 91is expressed as the transfer function matrix G_(I5), and therefore is alinear time-invariant process. The fifth-order harmonic compensationdoes not include nonlinear time-varying processes, i.e., the circuitdoes not include fixed-to-rotating coordinate conversion process norrotating-to-fixed coordinate conversion process. Hence, the entirecontrol loop is a linear time-invariant system. Therefore, thearrangement enables control system design and system analysis using alinear control theory. As described, use of the transfer function matrixG_(I5) represented by Equation (25) enables to replace the non-linearprocess in which fixed-to-rotating coordinate conversion is followed byI control and then by rotating-to-fixed coordinate conversion with alinear time-invariant multi-input multi-output system. This makes iteasy to perform system analysis and control system design.

The same applies to the seventh-order harmonic compensator 92 and theeleventh-order harmonic compensator 93. In other words the processesperformed in the seventh-order harmonic compensator 92 and in theeleventh-order harmonic compensator 93 are also linear time-invariantprocesses, and therefore it is possible to design control systems andperform system analyses using a linear control theory.

In the present embodiment, description was made for cases where elementsin a transfer function matrix have the same integral gain. However, eachelement in the matrix may be given a different value from others for itsintegral gain. For example, there may be a design to include additionalcharacteristics in the alpha axis component such as improved quickresponsiveness, improved stability, etc. Another example of adding acharacteristic may be to assign “0” to the integral gain K_(I) of theelement (1, 2) and that of the element (2, 1), to control both ofnegative-phase and negative-phase sequence components. Later,description will be made for a case of controlling both positive-phaseand negative-phase sequence components.

In the present embodiment, description was made for a case where thefifth-order harmonic compensator 91, the seventh-order harmoniccompensator 92 and the eleventh-order harmonic compensator 93 aredesigned individually from each other. However, the present invention isnot limited to this. The fifth-order harmonic compensator 91, theseventh-order harmonic compensator 92 and the eleventh-order harmoniccompensator 93 may be designed all in one, with a common integral gain.

In the seventh embodiment, description was made for cases where controlis made to positive phase sequence components in each harmonic. However,the present invention is not limited to this. Control may be made tonegative phase sequence components in each harmonic This can beaccomplished by using the transfer function matrix G_(In) used forcontrolling the positive phase sequence components in which the element(1, 2) and the element (2, 1) are swapped with each other. Also, controlmay be provided on both of the positive-phase and negative-phasesequence components. Hereinafter, description will be made for an eighthembodiment, where both positive-phase and negative-phase sequencecomponents are controlled.

As has been described earlier, the process shown in the transferfunction of the element (1, 1) and the element (2, 2) in the matrixG_(I) allows positive-phase and negative-phase sequence components topass through without changing their phase (see FIG. 7( a)). Therefore itis possible to provide control on both of the positive-phase andnegative-phase sequence components if use is made for the matrix G_(I)represented by Equation (12), in which “0” is assigned to the element(1, 2) and the element (2, 1). The same applies to the matrices G_(n)and G_(In): Therefore, it is possible to perform control on both of thepositive phase sequence component and the negative phase sequencecomponent if the element (1, 2) and the element (2, 1) are “0” in thematrices represented by Equations (23) and (24).

The eighth embodiment provides a control circuit, which is the controlcircuit 7 in FIG. 16 in which “0” is assigned to the element (1, 2) andthe element (2, 1) in matrices G_(I5), G_(I7), G_(I11) of the transferfunctions used in the fifth-order harmonic compensator 91, theseventh-order harmonic compensator 92, and the eleventh-order harmoniccompensator 93 respectively. Thus, the eighth embodiment can providecontrol on both positive-phase and negative-phase sequence components inharmonics of each order. Also, the eighth embodiment provides the sameadvantage as offered by the seventh embodiment, i.e., that theembodiment enables control system design and system analysis usinglinear control theories.

FIG. 17 is a diagram for describing a result of a simulation conductedwith the eighth embodiment.

In the simulation, non-balanced distortion and harmonic disturbance ineach order were added to the current in each phase in theinterconnection inverter system A (see FIG. 16), with a target currentset at 20 [A]. FIG. 17 shows waveforms of current signals Iu, Iv, Iwdetected by the current sensor 5 in an output current of each phase.FIG. 17( a) shows waveforms right after the simulation was startedwhereas FIG. 17( b) shows waveforms in 50 seconds after the simulationwas started. As shown in FIG. 17( b), each of the current signals Iu,Iv, Iw has a smooth waveform with all harmonic components suppressedwell.

FIG. 18 and FIG. 19 are diagrams for describing a result of anexperiment conducted with the eighth embodiment.

In this experiment, comparison was made between a case where there was aharmonic compensation controller 9 (including only a fifth-orderharmonic compensator 91 and a seventh-order harmonic compensator 92) wasprovided and a case the same was not provided in an interconnectioninverter system A (see FIG. 16) which was connected with an electricalpower system B contaminated with non-balanced distortion and harmonicdisturbance at each order of harmonics. FIG. 18 shows waveforms of aphase U current signal Iu after a steady state was achieved. FIG. 18( a)shows a case where the harmonic compensation controller 9 was notprovided whereas FIG. 18( b) shows a case where the harmoniccompensation controller 9 was provided. As compared to FIG. 18( a), thewaveform in FIG. 18( b) is smoother as a result of suppression on thefifth-order and the seventh-order harmonic components. FIG. 19 is achart which shows ratios of harmonic components contained in the currentsignals Iu, Iv, Iw in the steady state. The table shows percentagevalues of each harmonic component, with the fundamental wave componentbeing 100%. FIG. 18( a) shows a case where the harmonic compensationcontroller 9 was not provided whereas FIG. 18( b) shows a case where theharmonic compensation controller 9 was provided. As compared to thetable in FIG. 19( a), the table in FIG. 19( b) shows better suppressionon the fifth-order and the seventh-order harmonic components.

In the seventh and the eighth embodiments, description was made forcases where three current signals Iu, Iv, Iw are converted into an alphaaxis current signal Iα and a beta axis current signal Iβ, to providecontrol. However, the present invention is not limited to this. Forexample, control may be provided through direct use of the three currentsignals Iu, Iv, Iw. Hereinafter, such a case will be described as aninth embodiment.

FIG. 20 is a block diagram for describing a control circuit according tothe ninth embodiment. In this figure, elements which are identical withor similar to those in the control circuit 7″ in FIG. 11 are indicatedby the same reference codes.

FIG. 20 shows a control circuit 7″, which is the control circuit 7″ (seeFIG. 11) according to the third embodiment further including a harmoniccompensation controller 9′. The harmonic compensation controller 9′differs from the harmonic compensation controller 9 (see FIG. 16)according to the seventh embodiment in that its fifth-order harmoniccompensator 91′, seventh-order harmonic compensator 92′ andeleventh-order harmonic compensator 93′ provide direct control usingthree current signals Iu, Iv, Iw.

Since three-phase to two-phase conversion and two-phase to three-phaseconversion are expressed by Equation (1) and Equation (4), a process inwhich the three-phase to two-phase conversion is followed by the processrepresented by the transfer function matrix G_(n) and then followed bytwo-phase to three-phase conversion is expressed by a transfer functionmatrix G′_(n) represented by Equation (28) given below:

$\begin{matrix}{\begin{matrix}{G_{n}^{\prime} = {{\frac{2}{3}\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}{G_{n}\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}}} \\{= \begin{bmatrix}{G_{n\; 11}(s)} & {G_{n\; 12}(s)} & {G_{n\; 13}(s)} \\{G_{n\; 21}(s)} & {G_{n\; 22}(s)} & {G_{n\; 23}(s)} \\{G_{n\; 31}(s)} & {G_{n\; 32}(s)} & {G_{n\; 33}(s)}\end{bmatrix}}\end{matrix}{{{{where}\mspace{14mu} {when}\mspace{14mu} n} = {{3\; k} + {1\mspace{14mu} \left( {{k = 1},2,\ldots}\mspace{14mu} \right)}}},\begin{matrix}{{G_{n\; 11}(s)} = {G_{n\; 22}(s)}} \\{= {G_{n\; 33}(s)}} \\{= \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{3}}\end{matrix}}\begin{matrix}{{G_{n\; 12}(s)} = {G_{n\; 23}(s)}} \\{= {G_{n\; 31}(s)}} \\{= \frac{{\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; n\; \omega_{0}}} \right)}} + {\left( {{- 1} + {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; n\; \omega_{0}}} \right)}}}{6}}\end{matrix}\begin{matrix}{{G_{n\; 13}(s)} = {G_{n\; 21}(s)}} \\{= {G_{n\; 32}(s)}} \\{= \frac{{\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; n\; \omega_{0}}} \right)}} + {\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; n\; \omega_{0}}} \right)}}}{6}}\end{matrix}{{{when}\mspace{14mu} n} = {{3\; k} + {2\mspace{14mu} \left( {{k = 0},1,2,\ldots}\mspace{14mu} \right)}}}\begin{matrix}{{G_{n\; 11}(s)} = {G_{n\; 22}(s)}} \\{= {G_{n\; 33}(s)}} \\{= \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{3}}\end{matrix}\begin{matrix}{{G_{n\; 12}(s)} = {G_{n\; 23}(s)}} \\{= {G_{n\; 31}(s)}} \\{= \frac{{\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; n\; \omega_{0}}} \right)}} + {\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; n\; \omega_{0}}} \right)}}}{6}}\end{matrix}\begin{matrix}{{G_{n\; 13}(s)} = {G_{n\; 21}(s)}} \\{= {G_{n\; 32}(s)}} \\{= \frac{{\left( {{- 1} - {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; n\; \omega_{0}}} \right)}} + {\left( {{- 1} + {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; n\; \omega_{0}}} \right)}}}{6}}\end{matrix}} & (28)\end{matrix}$

Therefore, the process in which three-phase to two-phase conversion isfollowed by a process represented by the transfer function matrixG_(In), and then followed by two-phase to three-phase conversion isgiven by the matrix G′_(In) of the transfer function represented byEquation (29) given below:

$\begin{matrix}{{G_{In}^{\prime} = \begin{bmatrix}{G_{{In}\; 11}(s)} & {G_{{In}\; 12}(s)} & {G_{{In}\; 13}(s)} \\{G_{{In}\; 21}(s)} & {G_{{In}\; 22}(s)} & {G_{{In}\; 23}(s)} \\{G_{{In}\; 31}(s)} & {G_{{In}\; 32}(s)} & {G_{{In}\; 33}(s)}\end{bmatrix}}{{{{where}\mspace{14mu} {when}\mspace{14mu} n} = {{3\; k} + {1\mspace{14mu} \left( {{k = 1},2,\ldots}\mspace{14mu} \right)}}},\begin{matrix}{{G_{{In}\; 11}(s)} = {G_{{In}\; 22}(s)}} \\{= {G_{{In}\; 33}(s)}} \\{= {\frac{2}{3} \cdot \frac{K_{I}s}{s^{2} + {n^{2}\omega_{0}^{2}}}}}\end{matrix}}\begin{matrix}{{G_{{In}\; 12}(s)} = {G_{{In}\; 23}(s)}} \\{= {G_{{In}\; 31}(s)}} \\{= {{- \frac{1}{3}} \cdot \frac{K_{I}\left( {s + {\sqrt{3}n\; \omega_{0}}} \right)}{s^{2} + {n^{2}\omega_{0}^{2}}}}}\end{matrix}\begin{matrix}{{G_{{In}\; 13}(s)} = {G_{{In}\; 21}(s)}} \\{= {G_{{In}\; 32}(s)}} \\{= {{- \frac{1}{3}} \cdot \frac{K_{I}\left( {s - {\sqrt{3}n\; \omega_{0}}} \right)}{s^{2} + {n^{2}\omega_{0}^{2}}}}}\end{matrix}{{{when}\mspace{14mu} n} = {{3\; k} + {2\mspace{14mu} \left( {{k = 0},1,2,\ldots}\mspace{14mu} \right)}}}\begin{matrix}{{G_{{In}\; 11}(s)} = {G_{{In}\; 22}(s)}} \\{= {G_{{In}\; 33}(s)}} \\{= {\frac{2}{3} \cdot \frac{K_{I}s}{s^{2} + {n^{2}\omega_{0}^{2}}}}}\end{matrix}\begin{matrix}{{G_{{In}\; 12}(s)} = {G_{{In}\; 23}(s)}} \\{= {G_{{In}\; 31}(s)}} \\{= {{- \frac{1}{3}} \cdot \frac{K_{I}\left( {s - {\sqrt{3}n\; \omega_{0}}} \right)}{s^{2} + {n^{2}\omega_{0}^{2}}}}}\end{matrix}\begin{matrix}{{G_{{In}\; 13}(s)} = {G_{{In}\; 21}(s)}} \\{= {G_{{In}\; 32}(s)}} \\{= {{- \frac{1}{3}} \cdot \frac{K_{I}\left( {s + {\sqrt{3}n\; \omega_{0}}} \right)}{s^{2} + {n^{2}\omega_{0}^{2}}}}}\end{matrix}} & (29)\end{matrix}$

The fifth-order harmonic compensator 91′ receives three current signalsIu, Iv, Iw from the current sensor 5 for generation of fifth-orderharmonic compensation signals Yu₅, Yv₅, Yw₅ to be used in suppressingpositive phase sequence component of the fifth-order harmonic. Thecompensator performs a process represented by Equation (30) shown below.It should be noted here that the transfer function matrix G′_(I5) is thetransfer function matrix G′_(In) represented by Equation (29) with n=5.Also, the fifth-order harmonic compensator 91′ performs a stabilitymargin maximization process, which includes phase adjustment to correctphase delay in the control loop for reversing the phase. The currentsignals Iu, Iv, Iw represent “the first input signal”, “the second inputsignal”, and “the third input signal” according to the present inventionrespectively whereas the fifth-order harmonic compensation signals Yu₅,Yv₅, Yw₅ represent “the first output signal”, “the second output signal”and “the third output signal” according to the present inventionrespectively.

$\begin{matrix}{\begin{bmatrix}{Yu}_{5} \\{Yv}_{5} \\{Yw}_{5}\end{bmatrix} = {G_{I\; 5}^{\prime}\begin{bmatrix}{Iu} \\{Iv} \\{Iw}\end{bmatrix}}} & (30)\end{matrix}$

In the present embodiment, the fifth-order harmonic compensator 91′ isdesigned by H∞ loop shaping method, which is a method based on a linearcontrol theory, with a frequency weight being provided by the transferfunction matrix G′_(I5). The process performed in the fifth-orderharmonic compensator 91′ is expressed by the transfer function matrixG′_(I5), and therefore is a linear time-invariant process. Hence, it ispossible to perform control system design using a linear control theory.The fifth-order harmonic compensator 91′ is designed in the same manneras is the fifth-order harmonic compensator 91 according to the seventhembodiment. However, a linear control theory other than the H∞ loopshaping method may be utilized in the design.

The seventh-order harmonic compensator 92′ receives three currentsignals Iu, Iv, Iw from the current sensor 5 for generation ofseventh-order harmonic compensation signals Yu₇, Yv₇, Yw₇ to be used insuppressing positive phase sequence component in the seventh-orderharmonic. The compensator performs a process represented by the Equation(31) shown below. It should be noted here that the matrix G′_(I7) of thetransfer function is the transfer function matrix G′_(In) represented byEquation (29) with n=7. Also, the seventh-order harmonic compensator 92′performs a stability margin maximization process, which includes phaseadjustment to correct phase delay in the control loop for reversing thephase. The seventh-order harmonic compensator 92′ is also designed bythe same method as is the fifth-order harmonic compensator 91′.

$\begin{matrix}{\begin{bmatrix}{Yu}_{7} \\{Yv}_{7} \\{Yw}_{7}\end{bmatrix} = {G_{l\; 7}^{\prime}\begin{bmatrix}{Iu} \\{Iv} \\{Iw}\end{bmatrix}}} & (31)\end{matrix}$

The eleventh-order harmonic compensator 93′ receives three currentsignals Iu, Iv, Iw from the current sensor 5 for generation ofeleventh-order harmonic compensation signals Yu₁₁, Yv₁₁, Yw₁₁ to be usedin suppressing positive phase sequence components in the eleventh-orderharmonics. The compensator performs a process represented by thefollowing Equation (32). It should be noted here that the transferfunction matrix G′_(I11) is the transfer function matrix G′_(In)represented by Equation (29) with n=11. Also, the eleventh-orderharmonic compensator 93′ performs a stability margin maximizationprocess, which includes phase adjustment to correct phase delay in thecontrol loop for reversing the phase. The eleventh-order harmoniccompensator 93′ is also designed by the same method as is thefifth-order harmonic compensator 91′.

$\begin{matrix}{\begin{bmatrix}{Yu}_{11} \\{Yv}_{11} \\{Yw}_{11}\end{bmatrix} = {G_{l\; 11}^{\prime}\begin{bmatrix}{Iu} \\{Iv} \\{Iw}\end{bmatrix}}} & (32)\end{matrix}$

The fifth-order harmonic compensation signals Yα₅, Yβ₅ outputted fromthe fifth-order harmonic compensator 91′, the seventh-order harmoniccompensation signals Yα7, Yβ7 outputted from the seventh-order harmoniccompensator 92′, and the eleventh-order harmonic compensation signalsYα11, Yβ11 outputted from the eleventh-order harmonic compensator 93′are added together respectively, and the resulting harmonic compensationsignals Yu, Yv, Yw are outputted from the harmonic compensationcontroller 9. The harmonic compensation controller 9′ is designed inaccordance with the orders of harmonics which must be suppressed. Forexample, if it is desired to suppress only the fifth-order harmonics,then the controller may only include the fifth-order harmoniccompensator 91′. If it is desired to further suppress thethirteenth-order harmonic, then the controller should further include athirteenth-order harmonic compensator for a process expressed by atransfer function matrix G′_(I13), which is the transfer function matrixG_(In) of the transfer function represented by Equation (25) with n=13.

The harmonic compensation signals Yu, Yv, Yw outputted from the harmoniccompensation controller 9′ are added to the correction value signals Xu,Xv, Xw from the current controller 74″. After the addition of thecompensation signals Yu, Yv, Yw, system command values Ku, Kv, Kw fromthe system matching-fraction generator 72 are added to the correctionvalue signals Xu, Xv, Xw, to obtain command value signals X′u, X′v, X′w,which are then inputted to the PWM signal generator 77.

In the present embodiment, the process performed in the fifth-orderharmonic compensator 91′ is expressed by the transfer function matrixG′_(I5), and therefore is a linear time-invariant process. Also, thefifth-order harmonic compensation does not include nonlineartime-varying processes, i.e., the circuit does not includefixed-to-rotating coordinate conversion process nor rotating-to-fixedcoordinate conversion process. Hence, the entire control loop is alinear time-invariant system. Therefore, the arrangement enables controlsystem design and system analysis using a linear control theory. Thesame applies to the seventh-order harmonic compensator 92′ and theeleventh-order harmonic compensator 93′.

If negative phase sequence component control is to be performed in theninth embodiment, it can be achieved by using the transfer functionmatrix G′_(In) used for controlling the positive phase sequencecomponents in which the elements G_(In12)(s), G_(In23)(s), andG_(In31)(s) are swapped with G_(In13)(s), G_(In21)(s) and G_(In32)(s)respectively (specifically, a transposed matrix of the matrix G′_(In)should be used). Also, control may be provided on both positive-phaseand negative-phase sequence components. Hereinafter, description willcover such a case as a ninth embodiment, where the fifth-order harmoniccompensator 91′, the seventh-order harmonic compensator 92′, and theeleventh-order harmonic compensator 93′ control both positive-phase andnegative-phase sequence components.

If “0” is given to the element (1, 2) and the element (2, 1) of thematrix G_(n) in Equation (28) described above, the calculation providesa transfer function matrix G″_(n) represented by Equation (33) shownbelow:

$\begin{matrix}{G_{n}^{''} = {{\frac{2}{3}\begin{bmatrix}1 & 0 \\{- \frac{1}{2}} & \frac{\sqrt{3}}{2} \\{- \frac{1}{2}} & {- \frac{\sqrt{3}}{2}}\end{bmatrix}}{\quad{\begin{bmatrix}\frac{{F\left( {s + {{jn}\; \omega_{0}}} \right)} + {F\left( {s - {{jn}\; \omega_{0}}} \right)}}{2} & 0 \\0 & \frac{{F\left( {s + {{jn}\; \omega_{0}}} \right)} + {F\left( {s - {{jn}\; \omega_{0}}} \right)}}{2}\end{bmatrix} \times {\quad{\begin{bmatrix}1 & {- \frac{1}{2}} & {- \frac{1}{2}} \\0 & \frac{\sqrt{3}}{2} & {- \frac{\sqrt{3}}{2}}\end{bmatrix} = {\frac{1}{3} \cdot {\frac{{F\left( {s + {{jn}\; \omega_{0}}} \right)} + {F\left( {s - {{jn}\; \omega_{0}}} \right)}}{2}\begin{bmatrix}2 & {- 1} & {- 1} \\{- 1} & 2 & {- 1} \\{- 1} & {- 1} & 2\end{bmatrix}}}}}}}}} & (33)\end{matrix}$

Therefore, if the fifth-order harmonic compensator 91′ is to controlboth positive-phase and negative-phase sequence components, it can beaccomplished by using a transfer function matrix G″_(I5) which is thetransfer function matrix G″_(IN) represented by Equation (34) with n=5shown below. Likewise, if the seventh-order harmonic compensator 92′ isto control both positive-phase and negative-phase sequence components,it can be accomplished by using a transfer function matrix G″_(I7) whichis the transfer function matrix G″_(IN) represented by Equation (34)with n=7 shown below. Further, if the eleventh-order harmoniccompensator 93′ is to control both positive-phase and negative-phasesequence components, it can be accomplished by using a transfer functionmatrix G″_(I) 11 which is the transfer function matrix G″_(IN)represented by Equation (34) with n=11 shown below:

$\begin{matrix}{G_{\ln}^{''} = {\frac{1}{3} \cdot {\frac{K_{1}s}{s^{2} + {n^{2}\omega_{0}^{2}}}\begin{bmatrix}2 & {- 1} & {- 1} \\{- 1} & 2 & {- 1} \\{- 1} & {- 1} & 2\end{bmatrix}}}} & (34)\end{matrix}$

In the seventh through the ninth embodiments, description was made forcases where the fifth-order harmonic compensator 91 (91′), theseventh-order harmonic compensator 92 (92′) and the eleventh-orderharmonic compensator 93 (93′) perform a control which replaces Icontrol. However, the present invention is not limited by these. Forexample, an alternative control which replaces PI control may beprovided. If the fifth-order harmonic compensator 91, the seventh-orderharmonic compensator 92 and the eleventh-order harmonic compensator 93in the seventh embodiment are to provide an alternative control whichreplaces PI control, with n=3k+1 (k=1, 2, . . . ), it can beaccomplished by substituting ω₀ for n·ω₀ in the Equation (11) above,which will provide a transfer function matrix G_(PIn) represented byEquation (35) shown below. In a case where n=3k+2 (k=0, 1, 2, . . . ),then substitute the item ω₀ for n·ω₀ in Equation (11), swap the element(1, 2) with the element (2, 2) and use a transfer function matrixG_(PIn) represented by Equation (35′) shown below. The followingEquations (35) and (35′) can be obtained by substituting F(s) forK_(P)+K_(I)/s in Equations (23) and (23′).

$\begin{matrix}{G_{P\mspace{14mu} \ln} = \begin{bmatrix}\frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{{- K_{l}}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} \\\frac{K_{l}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{{K_{P}s^{2}} + {K_{l}s} + {K_{p}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}\end{bmatrix}} & (35) \\{G_{P\mspace{14mu} \ln} = \begin{bmatrix}\frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{K_{l}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} \\\frac{{- K_{l}}n\; \omega_{0}}{s^{2} + {n^{2}\omega_{0}^{2}}} & \frac{{K_{P}s^{2}} + {K_{l}s} + {K_{p}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}\end{bmatrix}} & \left( 35^{\prime} \right)\end{matrix}$

If the fifth-order harmonic compensator 91 is to provide control whichreplaces PI control, it can be accomplished by using a matrix G_(PI5)represented by Equation (35′) with n=5. If the seventh-order harmoniccompensator 92 is to provide control which replaces PI control, it canbe accomplished by using a matrix G_(PI7) given by Equation (35′) withn=7. If the eleventh-order harmonic compensator 93 is to provide controlwhich replaces PI control, it can be accomplished by using a matrixG_(PI11) given by Equation (35′) with n=11.

If the fifth-order harmonic compensator 91, the seventh-order harmoniccompensator 92 and the eleventh-order harmonic compensator 93 in theeighth embodiment are to provide control which replaces PI control, itcan be accomplished by using the transfer function matrix G_(PIn)represented by Equations (35) and (35′) in which “0” is given to theelement (1, 2) and the element (2, 1).

If the fifth-order harmonic compensator 91′, the seventh-order harmoniccompensator 92′ and the eleventh-order harmonic compensator 93′ in theninth embodiment are to provide control which replaces PI control, itcan be accomplished by using a transfer function matrix G′_(PIn)represented by Equation (36) shown below:

$\begin{matrix}{G_{P\mspace{14mu} \ln}^{\prime} = \begin{bmatrix}{G_{{Pln}\; 11}(s)} & {G_{{Pln}\; 21}(s)} & {G_{{Pln}\; 31}(s)} \\{G_{{Pln}\; 21}(s)} & {G_{{Pln}\; 22}(s)} & {G_{{Pln}\; 23}(s)} \\{G_{{Pln}\; 31}(s)} & {G_{{Pln}\; 32}(s)} & {G_{{Pln}\; 33}(s)}\end{bmatrix}} & (36)\end{matrix}$

where when n=3k+1 (k=1, 2, . . . ),

${G_{{Pln}\; 11}(s)} = {{G_{{Pln}\; 22}(s)} = {{G_{{Pln}\; 33}(s)} = {\frac{2}{3} \cdot \frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}}}}$${G_{{Pln}\; 12}(s)} = {{G_{{Pln}\; 23}(s)} = {{G_{{Pln}\; 31}(s)} = {{- \frac{1}{3}} \cdot \frac{{K_{P}s^{2}} + {K_{l}\left( {s + {\sqrt{3}n\; \omega_{0}}} \right)} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}}}}$${G_{{Pln}\; 13}(s)} = {{G_{{Pln}\; 21}(s)} = {{G_{{Pln}\; 32}(s)} = {{- \frac{1}{3}} \cdot \frac{{K_{P}s^{2}} + {K_{l}\left( {s - {\sqrt{3}n\; \omega_{0}}} \right)} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}}}}$when  n = 3k + 2  (k = 0, 1, 2, …)${G_{{Pln}\; 11}(s)} = {{G_{{Pln}\; 22}(s)} = {{G_{{Pln}\; 33}(s)} = {\frac{2}{3} \cdot \frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}}}}$${G_{{Pln}\; 12}(s)} = {{G_{{Pln}\; 23}(s)} = {{G_{{Pln}\; 31}(s)} = {{- \frac{1}{3}} \cdot \frac{{K_{P}s^{2}} + {K_{l}\left( {s - {\sqrt{3}n\; \omega_{0}}} \right)} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}}}}$${G_{{Pln}\; 13}(s)} = {{G_{{Pln}\; 21}(s)} = {{G_{{Pln}\; 32}(s)} = {{- \frac{1}{3}} \cdot \frac{{K_{P}s^{2}} + {K_{l}\left( {s + {\sqrt{3}n\; \omega_{0}}} \right)} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}}}}$

If the fifth-order harmonic compensator 91′, the seventh-order harmoniccompensator 92′, and the eleventh-order harmonic compensator 93′ are toprovide control which replaces PI control, in the configuration thatnegative phase sequence component control is performed for each harmonicin the ninth embodiment, it can be achieved by using a matrix providedby the transfer function matrix G′_(PIn) represented by Equation (36)above in which the elements G_(PIn12)(s), G_(PIn23)(s) and G_(PIn31)(s)are swapped with G_(PIn13)(s), G_(PIn21)(s) and G_(PIn32)(s)respectively (specifically, a transposed matrix of the matrix G′_(PIn)should be used). Also, if the fifth-order harmonic compensator 91′, theseventh-order harmonic compensator 92′ and the eleventh-order harmoniccompensator 93′ are to provide alternative control which replaces PIcontrol, in the configuration that both positive-phase andnegative-phase sequence components are controlled in the ninthembodiment, it can be accomplished by using a transfer function matrixG″_(PIn) represented by Equation (37) shown below:

$\begin{matrix}{G_{Pln}^{''} = {\frac{1}{3} \cdot {\frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}\begin{bmatrix}2 & {- 1} & {- 1} \\{- 1} & 2 & {- 1} \\{- 1} & {- 1} & 2\end{bmatrix}}}} & (37)\end{matrix}$

Providing alternative control which replaces PI control provides anadvantage that a damping effect can be added at transient time byadjusting the proportional gain K_(P). However, there is also adisadvantage that the system is more sensitive to modeling errors. Onthe contrary, providing control which replaces I control isdisadvantageous in that a damping effect at transient time cannot beadded, yet there is an advantage that the system is not very muchsensitive to modeling errors.

Still another alternative may be that the fifth-order harmoniccompensator 91 (91′), the seventh-order harmonic compensator 92 (92′)and the eleventh-order harmonic compensator 93 (93′) perform alternativecontrol which replaces the above-described other alternative controlsequivalent to I control or to the PI control. If transfer functions F(s)in Equations (23) and (23′) are substituted for a transfer functions ofthe above-mentioned alternative control, it becomes possible tocalculate a transfer function matrix which represents a processequivalent to carrying out fixed-to-rotating coordinate conversion, thenthe above-described alternative control and then rotating-to-fixedcoordinate conversion. Therefore, it is possible to design a systemwhich provides an alternative control to PID control (the transferfunction for which is expressed as F(s)=K_(P)+K_(I)/s+K_(D)·s, whereproportional gain is represented by K_(P), integral gain is representedby K_(I), and derivative gain is represented by K_(D)). It is alsopossible to provide controls which can substitute D control (derivativecontrol; the transfer function for which is expressed as F(s)=K_(D)·s,where derivative gain is represented by K_(D)); P control (proportionalcontrol; the transfer function for which is expressed as F(s)=K_(P),where proportional gain is represented by K_(P)); PD control; IDcontrol; etc.

In the seventh through the ninth embodiments thus far, description wasmade for cases where output current is controlled. However, the presentinvention is not limited to this. For example, output voltage may becontrolled. In this case, the control circuit 8 (see FIG. 13) accordingto the fourth embodiment further includes the harmonic compensationcontroller 9. Again, the arrangement provides the same advantages asoffered by the seventh embodiment. Also, any of the control methodsdescribed thus far for the seventh through the ninth embodiments isapplicable to the case where output voltage is controlled. For example,both of positive-phase and negative-phase sequence components may becontrolled; three voltage signals Vu, Vv, Vw may be used for control; oralternative control replacing PI control may be provided. Also, theremay be a configuration where the control circuit 8′ (see FIG. 14)according to the fifth embodiment further includes the harmoniccompensation controller 9.

Next, description will cover methods for preventing harmonic suppressioncontrol from becoming divergent.

In the seventh embodiment (see FIG. 16), the fifth-order harmoniccompensator 91 performs phase adjustment to correct phase delay in thecontrol loop for reversing the phase. Setting for the phase adjustmentis based on the impedance of the interconnection inverter system A(mainly from a reactor inductance and capacitor capacitance of thefilter circuit 3) before the system is interconnected with theelectrical power system B. Once the interconnection inverter system A isconnected with the electrical power system B and if the electrical powersystem B has load conditions which are different from the assumption,there can be a problem such as a shift or an increase in resonancepoints of the filter circuit 3. If this happens, phase correction is nolonger appropriate, and the control can be divergent.

FIG. 21 is a Bode diagram of a transfer function from an output voltageof the inverter circuit 2 to an output current of the interconnectioninverter system A, showing an example of the transfer function beforeand after the interconnection inverter system A is connected with theelectrical power system B.

With the system voltage fundamental wave angular frequency ω₀ being 120π[rad/sec] (60 [Hz]), angular frequency of the fifth-order harmonic is600π (≈1885) [rad/sec] (300 [Hz]). According to FIG. 21, the phase ofthe fifth-order harmonic is delayed by about 90 degrees before theconnection, but delayed by about 270 degrees after the connection. Inother words, even if the phase adjustment for negative feedback controlis made before the connection, the control will become positive feedbackcontrol after the connection and therefore the control will becomedivergent. Hereinafter, a tenth embodiment will cover an arrangementincluding a configuration for preventing such a control divergence.

FIG. 22 is a drawing for describing a harmonic compensation controlleraccording to the tenth embodiment. The figure shows a fifth-orderharmonic compensator 91 and a divergence preventer disposed on thesubsequent stage.

The divergence preventer 94 works for preventing the fifth-orderharmonic suppression control from becoming divergent. If the divergencepreventer 94 determines that the control tends to be divergent, then thedivergence preventer 94 changes the phase of the fifth-order harmoniccompensation signals Yα₅, Yβ₅ inputted from the fifth-order harmoniccompensator 91, and outputs the changed signals. The divergencepreventer 94 includes a divergence determiner 941 and a phase changer942.

The divergence determiner 941 determines whether or not the control hasa divergent tendency. The divergence determiner 941 compares thefifth-order harmonic compensation signal Yα₅ (or the fifth-orderharmonic compensation signal Yβ₅) from the fifth-order harmoniccompensator 91 with a predetermined threshold value, and if thefifth-order harmonic compensation signal Yα₅ is greater than thepredetermined threshold value, it determines that the control has adivergent tendency. Upon determination that the control has a divergenttendency, the divergence determiner 941 outputs a judge signal to thephase changer 942. It should be noted here that the divergencedeterminer 941 may determine the divergent tendency by a differentmethod. For example, the determiner may determine that the control has adivergent tendency if the fifth-order harmonic compensation signals Yα₅remains greater than a predetermined threshold value for a predeterminedamount of time. Another method may be that a maximum value of thefifth-order harmonic compensation signal Yα₅ is always stored and agradient of the maximum value is utilized as a base of determining ifthe control has a divergent tendency.

The phase changer 942 changes the phase of the fifth-order harmoniccompensation signals Yα₅, Yβ₅ inputted from the fifth-order harmoniccompensator 91, and outputs the changed signals. The phase changer 942performs a process represented by Equation (38) shown below, to outputfifth-order harmonic compensation signals Y′α₅, Y′β₅:

$\begin{matrix}{\begin{bmatrix}{Y^{\prime}\alpha_{5}} \\{Y^{\prime}\beta_{5}}\end{bmatrix} = {\begin{bmatrix}{\cos \; {\Delta\theta}_{5}} & {{- \sin}\; {\Delta\theta}_{5}} \\{\sin \; {\Delta\theta}_{5}} & {\cos \; {\Delta\theta}_{5}}\end{bmatrix}\begin{bmatrix}{Y\; \alpha_{5}} \\{Y\; \beta_{5}}\end{bmatrix}}} & (38)\end{matrix}$

The item Δθ₅ has an initial value of “0”, so the fifth-order harmoniccompensation signals Yα₅, Yβ₅ are outputted without any phase changeuntil there is an input of the judge signal from the divergencedeterminer 941. When there is an input of the judge signal from thedivergence determiner 941, the phase changer 942 varies Δθ₅, therebychanging the phase and then outputs the changed fifth-order harmoniccompensation signals Y′α₅, Y′β₅. When the input of the judge signal fromthe divergence determiner 941 ceases, the phase changer 942 fixes thevalue of Δθ₅. Thus, the phase changer 942 changes the phase and outputthe changed fifth-order harmonic compensation signals Y′α₅, Y′β₅. Ifvarying the Δθ₅ (e.g., increasing the value thereof) gives a greatervalue to the fifth-order harmonic compensation signals Yα₅, then thephase changer 942 varies the Δθ₅ in reverse direction (e.g., decreasingthe value thereof), to search for a value for Δθ₅ to converge thecontrol.

If the control has a divergent tendency, Δθ₅ is varied in search for anappropriate Δθ₅ while if the control does not have a divergent tendencyΔθ₅ is fixed to output the fifth-order harmonic compensation signalsY′α₅, Y′β₅ in which appropriate adjustment has been made to the phase.Thus, the arrangement prevents the control from becoming divergent.

However, the configuration for control divergence prevention is notlimited to the above. Divergence in control may be prevented by othermethods.

FIG. 23 is a drawing for describing a harmonic compensation controlleraccording to another example of the tenth embodiment. The figure shows afifth-order harmonic compensator 91 and a divergence preventer disposedon the subsequent stage.

A divergence preventer 94′ works for preventing the fifth-order harmonicsuppression control from becoming divergent. If the divergence preventer94′ determines that the control tends to be divergent, then thedivergence preventer 94′ stops outputting the fifth-order harmoniccompensation signals Yα₅, Yβ₅ received from the fifth-order harmoniccompensator 91. The divergence preventer 94′ differs from the divergencepreventer 94 in FIG. 22 in that it includes an output stopper 943 inplace of the phase changer 942.

The output stopper 943 outputs the fifth-order harmonic compensationsignals Yα₅, Yβ₅ as it receives as long as there is no input of thejudge signal from the divergence determiner 941. If there is an input ofthe judge signal from the divergence determiner 941, the output stopper943 stops outputting the fifth-order harmonic compensation signals Yα₅,Yβ₅.

If the control does not have a divergent tendency, the fifth-orderharmonic compensation signals Yα₅, Yβ₅ inputted from the fifth-orderharmonic compensator 91 are outputted as are, whereas if the control hasa divergent tendency, the output of the fifth-order harmoniccompensation signals Yα₅, Yβ₅ is stopped. Without the output of thefifth-order harmonic compensation signals Yα₅, Yβ₅, the fifth-orderharmonic suppression control ceases and therefore the arrangementprevents the control from becoming divergence. The lack of thefifth-order harmonic suppression control does not affect the othercontrols.

It should be noted here that the phase changer 942 shown in FIG. 22 maybe provided before the output stopper 943, so that search for a Δθ₅ maybe performed while the fifth-order harmonic suppression control isceased and the output stopper 943 is resumed once the Δθ₅ is determined.

The seventh-order harmonic compensator 92 and the eleventh-orderharmonic compensator 93 may include the same arrangement to preventdivergence in each harmonic suppression control. Also, the eighth andthe ninth embodiments may have the same arrangement to prevent harmonicsuppression control from becoming divergent at each harmonic level.

In the seventh through the tenth embodiment thus far, description wasmade for cases where the harmonic compensation controller 9 is added tothe control circuit of the interconnection inverter system (invertersystem). However, the present invention is not limited to these. Forexample, the harmonic compensation controller 9 (9′) may be added tocontrol circuits for harmonic compensation devices, power activefilters, unbalanced compensators, static var compensators (SVC, SVG) anduninterruptable power supply systems (UPS). Also, the control circuitmay provide harmonic compensation only without controlling thefundamental waves (i.e., the circuit may not include the currentcontroller). For example, the harmonic compensator is implemented bywhichever of the arrangements shown in FIG. 16 and FIG. 20, if thearrangement does not include the current controller 74 (74″). Thecircuit will then be dedicated to harmonic suppression by the harmoniccompensation controller 9 (9′). Further, the idea of adding the harmoniccompensation controller 9 (9′) is not limited to those control circuitsfor controlling inverter circuits which convert DC current intothree-phase AC current. For example, the harmonic compensationcontroller 9 (9′) may be added to control circuits for convertercircuits (see the sixth embodiment in FIG. 15) which convert three-phaseAC current into DC current, for cyclo-converters which convertthree-phase AC frequencies, etc.

Next, description will cover a case where the control circuit accordingto the present invention is applied to a control circuit of a motordriving inverter circuit. Motor driving inverter circuits are aninverter circuit for driving AC motors (e.g., induction motors andsynchronous motors), i.e., electric motors which are driven by AC power.

A typical control circuit in a conventional motor-drive inverter circuitreceives current signals I detected by a current sensor, an angularfrequency ω₀ and a phase θ calculated by a rotation-speed/positiondetection circuit as inputs, generates PWM signals based on these, andoutputs the PWM signals to the inverter circuit. Therotation-speed/position detection circuit detects rotation speed androtation position of the motor's rotor, and uses this information tocalculate the angular frequency ω₀ and the phase θ for use in thecontrol provided by the control circuit.

AC motors are used in a variety of fields and there is an increasingdemand for high-speed rotation in recent years for purposes of higheroutput, wider operation speed range, etc. For AC motors to be able toachieve high-speed rotation, stable current control is essential.Conventionally, control circuits for motor driving inverter circuitsprovide a control which is based on rotating coordinate system, and thisposes a technical problem of interference between the d axis controlsystem and the q axis control system. The interference between the daxis control system and the q axis control system caused by the motor'sinductance destabilizes the current control, and in order to suppressthe interference, adjustment is performed by calculating an amount ofinterference by using a non-interference portion.

However, it is difficult to accurately identify the motor inductance.Consequently, as the angular frequency ω₀ increases with increase in themotor speed, the amount of interference which is calculated by using thenon-interference portion has an increased error. This leads to unstablenon-interference process, which then leads to unstable control by thecontrol circuit. Another problem is that it is not possible to designthe control system by a linear control theory since the conventionalcontrol is based on a nonlinear time-varying process. For these reasons,it has been difficult to design a control system which provides both ofrapid response and stability.

Hereinafter, a motor driving unit will be described as an eleventhembodiment in which a current controller which provides a processexpressed by the transfer function matrix G_(I) represented by Equation(12) is applied to a control circuit of a motor driving inverter circuitfor providing control based on a fixed coordinate system.

FIG. 24 is a block diagram for describing a motor driving unit accordingto the eleventh embodiment. In this figure, elements which are identicalwith or similar to those in the interconnection inverter system A inFIG. 1 are indicated by the same reference codes.

As shown in the figure, a motor driving unit D includes an invertercircuit 2 and a control circuit 10, converts DC power from a DC powersource 1 into AC power, and supplies the AC power to a motor M. Theinverter circuit 2 has a current sensor 5 in its output line. Thecurrent sensor 5 detects a current which is flowing in a motor windingwire of each phase in the motor M. The control circuit 10 providescontrol so that the current signals detected by the current sensor 5will be equal to target values. The motor M is provided with a rotatingspeed detection circuit 11, which detects a rotating speed of the rotorof the motor M and calculates the angular frequency ω₀.

The DC power source 1 outputs DC power by, e.g., converting AC powerfrom the electrical power system into DC power using a converter, arectifier, etc. It may include batteries, fuel cells, electric doublelayer capacitor, lithium-ion batteries or solar cells.

The inverter circuit 2 converts a DC voltage from the DC power source 1into an AC voltage, and outputs the AC voltage. The inverter circuit 2,which includes an unillustrated PWM-control three-phase inverter havingsix switching elements in three sets, switches ON and OFF each of theswitching elements based on PWM signals from the control circuit 10,thereby converting the DC voltage from the DC power source 1 into ACvoltages.

The motor M is an electric motor which utilizes three-phase AC power andis provided by, e.g., a three-phase induction motor or a three-phasesynchronous motor. The current sensor 5 detects an AC current of eachphase outputted from the inverter circuit 2 (Specifically, it detects acurrent which flows into the winding wire of each phase in the motor M).The detected current signals I (Iu, Iv, Iw) are inputted to the controlcircuit 10. The rotating speed detection circuit 11 detects the rotor'srotating speed in the motor M by means of encoder for example, adds aslip angular velocity to the detected rotating speed, therebycalculating the angular frequency ω₀. The detected angular frequency ω₀is inputted to the control circuit 10. Alternatively, however, therotating speed detection circuit 11 may detect and output a rotorrotating speed of the motor M to the control circuit 10 so that theangular frequency ω₀ is calculated by the control circuit 10.

The control circuit 10 controls the inverter circuit 2, and isimplemented by a microcomputer for example. The control circuit 10differs from the control circuit 7 (see FIG. 6) according to the firstembodiment, in that the angular frequency ω₀ is inputted from therotating speed detection circuit 11 and that it does not have the systemmatching-fraction generator 72.

In the present embodiment, the control circuit 10 performs control inthe fixed coordinate system without making fixed-to-rotating coordinateconversion nor rotating-to-fixed coordinate conversion. Therefore, nointerference is caused to the control due to the inductance. Hence, itis possible to provide stable control even when the motor M is rotatingat a high speed. Also, since the inductance causes no interference withthe control, there is no need to provide a non-interference portion.Also, as has been described earlier, the transfer function matrix G_(I)is a transfer function matrix which shows a process equivalent tocarrying out fixed-to-rotating coordinate conversion, I control and thenrotating-to-fixed coordinate conversion.

Since the process performed in the current controller 74 is expressed asa transfer function matrix G_(I), it is a linear time-invariant process.Also, the control circuit 10 does not include nonlinear time-varyingprocesses, i.e., the circuit does not include fixed-to-rotatingcoordinate conversion process nor rotating-to-fixed coordinateconversion process. Hence, the entire current control system is a lineartime-invariant system. Therefore, the arrangement enables control systemdesign and system analysis using a linear control theory. Since it isnow possible to design control systems which provides both rapidresponse and stability, it is now possible to provide stable controlwith rapid response. As described, use of the transfer function matrixG_(I) represented by Equation (12) enables to replace the non-linearprocess in which fixed-to-rotating coordinate conversion is followed byI control and then by rotating-to-fixed coordinate conversion with alinear time-invariant multi-input multi-output system. This makes iteasy to perform system analysis and control system design.

It should be noted here that variations described for the first throughthe third embodiments are also applicable to the present embodiment.Namely, control may be made to negative phase sequence component of thefundamental wave component in the current signals I (Iu, Iv, Iw);control may be made to both positive-phase and negative-phase sequencecomponents; or control may be made directly by using three currentsignals Iu, Iv, Iw. Also, the current controller 74 may providealternative control which replaces PI control or other controls.

When a motor is driven by an inverter, harmonic components are sometimescontained in electric currents which flow through the motor. Causes ofthe harmonic components include dead time which is added during PWMsignal generation, imbalance or offset in the current sensor, voltageswing in the DC voltage which is outputted from the DC power source,structure of the motor, etc. Harmonic component inclusion in motordriving can cause over current, operating noise, reduced performance incontrol, etc. Therefore, it is necessary to suppress harmoniccomponents. Hence, as has been described for the seventh through thetenth embodiments, the control circuit 10 may include the harmoniccompensation controller 9 (9′) to suppress harmonic components. In thiscase, the rotating speed detection circuit 11 also supplies the angularfrequency ω₀ for use by the harmonic compensation controller 9 (9′).

Next, methods for compensating for torque ripples will be described.

In motor torque control, quality of torque generated is an importantfactor. Like harmonics, torque ripples are caused by dead time which isadded during PWM signal generation, imbalance or offset in the currentsensor, voltage swing in the DC voltage which is outputted from the DCpower source, structure of the motor, etc. As a method for removing thisperiodic ripples in the torque, an appropriate compensation signal(hereinafter will be called “torque ripple compensation signal”) may besuperimposed on an electric-current target value of each torque commandfor compensation for torque ripples. Generally, the torque ripplecompensation signals are harmonic components of the fifth-, seventh-,eleventh-, and other orders. Therefore, harmonic compensation by theharmonic compensation controller 9 (see FIG. 16) may be replaced bycontrol which follows the torque ripple compensation signal.Specifically, instead of inputting the alpha axis current signal Iα andthe beta axis current signal Iβ to the harmonic compensation controller9, deviations of the alpha axis current signal Iα and the beta axiscurrent signal Iβ from their respective target values are inputted.

The fifth-order harmonic compensator 91, the seventh-order harmoniccompensator 92 and the eleventh-order harmonic compensator 93 are allsupplied with deviations ΔIα, ΔIβ of the alpha axis current signal Iαand the beta axis current signal Iβ from the alpha axis current targetvalue and the beta axis current target value respectively, but each ofthe harmonic compensators 91, 92, 93 controls harmonic componentcorresponding only to their amplitude characteristic (see FIG. 7).Therefore, in the fifth-order harmonic compensator 91 for example, thefifth-order harmonic component contained in the alpha axis currentsignal Iα and in the beta axis current signal Iβ are controlled tofollow the fifth-order harmonic component of the torque ripplecompensation signal superimposed on the alpha axis current target valueand beta axis current target value. Thus, the current which flows fromthe inverter circuit 2 to the motor M follows the current target valuewhich is superimposed with the torque ripple compensation signal,whereby periodic ripples in the torque are removed. The same applies tocases where direct control is performed by using three current signalsIu, Iv, Iw. Namely, deviations of the current signals Iu, Iv, Iw fromtheir respective target values are inputted to the harmonic compensationcontroller 9′ (see FIG. 20) instead of inputting the current signals Iu,Iv, Iw.

In the first through the eleventh embodiments, description was made forcases where the inverter circuit 2 is provided by a three-phase invertercircuit and power is supplied to a three-phase electrical power system Bor a three-phase AC motor. However, the present invention is not limitedto these. The control circuit according to the present invention is alsoapplicable to cases where a single-phase inverter circuit supplies powerto a single-phase electrical power system or a single-phase AC motor.Hereinafter, description will cover a twelfth embodiment where thepresent invention is applied to a control circuit of a single-phaseinverter circuit in a single-phase interconnection inverter system.

FIG. 25 is a block diagram for describing a single-phase interconnectioninverter system according to the twelfth embodiment. In this figure,elements which are identical with or similar to those in theinterconnection inverter system A (see FIG. 6) according to the firstembodiment are indicated by the same reference codes.

As shown in the figure, an interconnection inverter system E includes aDC power source 1, an inverter circuit 2″, a filter circuit 3, a voltagetransformer circuit 4, a current sensor 5, a voltage sensor 6, and acontrol circuit 12. The inverter circuit 2″ is a single-phase inverterprovided by a PWM control inverter circuit which includes unillustratedfour switching elements in two sets. The interconnection inverter systemE converts DC power from the DC power source 1 into AC power, for supplyto a single-phase AC electrical power system B′.

The control circuit 12 differs from the control circuit 7 (see FIG. 6)according to the first embodiment in that it does not include thethree-phase to two-phase converter 73 and the two-phase to three-phaseconverter 76, and that it includes the alpha axis current controller 74′(see FIG. 9) according to the second embodiment in place of the currentcontroller 74.

The alpha axis current controller 74′ receives a deviation between asingle-phase current signal (alpha axis current signal) detected by thesingle-phase current sensor 5 and its target value, i.e., an alpha axiscurrent target value. The alpha axis current controller 74′ performs aprocess given by a transfer function G_(I)(s) represented by thefollowing Equation (39), which expresses the element (1, 1) and theelement (2, 2) in the matrix G_(I) and outputs a compensation valuesignal X. In a single-phase system, the process needs to be performedonly to the alpha axis current signal, so it is not necessary togenerate a signal which has a 90-degree phase delay.

$\begin{matrix}{{G_{l}(s)} = \frac{K_{l}s}{s^{2} + \omega_{0}^{2}}} & (39)\end{matrix}$

As has been described earlier, the alpha axis current controller 74′ isdesigned by H∞ loop shaping method, which is a method based on linearcontrol theory, with a frequency weight being provided by the transferfunction G_(I)(s). Since the process performed in the alpha axis currentcontroller 74′ is expressed as a transfer function G_(I)(s), it is alinear time-invariant process. Hence, it is possible to perform controlsystem design using a linear control theory. It should be noted herethat a linear control theory other than the H∞ loop shaping method maybe utilized in the design.

The system command value K from the system matching-fraction generator72 and the correction value signal X from the alpha axis currentcontroller 74′ are added to each other, to obtain a command valuesignals X′, which is then inputted to the PWM signal generator 77′.

The PWM signal generator 77′ generates PWM signals Pp, Pn by trianglewave comparison method based on the command value signal X′ inputted, asignal provided by inverting the command value signal X′ and a carriersignal which is generated as a triangle-wave signal at a predeterminedfrequency (e.g. 4 kHz). The generated PWM signals Pp, Pn are outputtedto the inverter circuit 2″. The PWM signal generator 77′ also outputssignals which are provided by inverting the PWM signal Pp, Pn, to theinverter circuit 2″.

The present embodiment provides the same advantages as offered by thefirst embodiment. Also, since the control circuit 12 does not need thesignal which has a 90-degree phase delay from the alpha axis currentsignal, there is no need for an arrangement to generate a signal whichhas a 90-degree phase delay. Further, since the process is performedonly to the alpha axis current signal (since there is no need forprocessing the signal with a 90-degree phase delay), the embodimentprovides a simple configuration.

Like the fourth and the fifth embodiment, the twelfth embodiment may usean arrangement to control output voltage. Also, like in the sixthembodiment, the control circuit 12 may be used for a control circuit ofa converter circuit which converts a single-phase AC into DC. Also, thealpha axis current controller 74′ may provide alternative control whichreplaces PI control or other controls. Further, the present embodimentmay be applied to the eleventh embodiment, i.e. driving of AC motors fordriving single-phase AC motors.

Still further, like the seventh through the tenth embodiments, thecontrol circuit 12 may include a harmonic compensation controller forsuppression of harmonic components. Hereinafter, a thirteenth embodimentwill cover such a case where a harmonic compensation controller isincluded in the control circuit 12 of the single-phase inverter circuit2″.

The transfer function G_(I)(s) represented by Equation (39) above is forcontrol of fundamental wave components. The n-th harmonic is an angularfrequency component obtained by multiplying the fundamental wave angularfrequency by n. Therefore, a transfer function for controlling then-th-order harmonic is given as a transfer function G_(In)(s)represented by Equation (40) shown below, which is Equation (39) withthe item ω₀ substituted for n·ω₀. Equation (40) expresses the element(1, 1) and the element (2, 2) in the matrix G_(In) represented byEquations (24), (24′).

$\begin{matrix}{{G_{\ln}(s)} = \frac{K_{l}s}{s^{2} + \left( {n \cdot \omega_{0}} \right)^{2}}} & (40)\end{matrix}$

FIG. 26 is a block diagram for describing an interconnection invertersystem according to a thirteenth embodiment. In this figure, elementswhich are identical with or similar to those in the control circuit 12in FIG. 25 are indicated by the same reference codes. FIG. 26 shows acontrol circuit 12, which is the control circuit 12 (see FIG. 25)according to the twelfth embodiment further including a harmoniccompensation controller 9″.

The harmonic compensation controller 9″ receives a current signal Idetected by the current sensor 5, and generates a harmonic compensationsignal Y for the harmonic suppression control. The harmonic compensationcontroller 9″ includes a fifth-order harmonic compensator 91″ forsuppressing the fifth-order harmonic, a seventh-order harmoniccompensator 92″ for suppressing the seventh-order harmonic and aneleventh-order harmonic compensator 93″ for suppressing theeleventh-order harmonic.

The fifth-order harmonic compensator 91″ works for suppressing thefifth-order harmonic. The fifth-order harmonic compensator 91″ performsa process given by a transfer function G_(I5)(s), which is the transferfunction G_(In)(s) expressed by Equation (40) with n=5 for the controlof the fifth-order harmonic. In other words, the fifth-order harmoniccompensator 91″ performs a process represented by the following Equation(41), to output fifth-order harmonic compensation signal Y₅. As for theangular frequency ω₀, a predetermined value is set as an angularfrequency (for example, ω₀=120π [rad/sec] (60 [Hz])) for the systemvoltage fundamental wave, and the integral gain K_(I5) is a pre-designedvalue. Also, the fifth-order harmonic compensator 91″ performs astability margin maximization process, which includes phase adjustmentto correct a phase delay in the control loop for reversing the phase.The current signal I represents the “input signal” according to thepresent invention whereas the fifth-order harmonic compensation signalY5 represents the “output signal” according to the present invention.

$\begin{matrix}{Y_{5} = {{{G_{l\; 5}(s)}I} = {\frac{K_{l\; 5}s}{s^{2} + {25\omega_{0}^{2}}}I}}} & (41)\end{matrix}$

In the present embodiment, the fifth-order harmonic compensator 91″ isdesigned by H∞ loop shaping method, which is a method based on a linearcontrol theory, with a frequency weight being provided by the matrixG_(I5)(s) of the transfer function. The process performed in thefifth-order harmonic compensator 91″ is expressed as the matrixG_(I5)(s) of the transfer function, and therefore is a lineartime-invariant process. Hence, it is possible to perform control systemdesign using a linear control theory.

It should be noted here that design method to be used in designing thecontrol system is not limited to this. In other words, other linearcontrol theories may be employed for the design. Examples of usablemethods include loop shaping method, optimum control, H∞ control, mixedsensitivity problem, and more. Also, there may be an arrangement that aphase θ₅ is calculated and set in advance for adjustment based on thephase delay. For example, if the target of control has a 90-degree phasedelay, a 180-degree phase delay may be designed by a setting of θ₅=−90degrees.

The seventh-order harmonic compensator 92″ works for suppressing theseventh-order harmonic. The seventh-order harmonic compensator 92″performs a process expressed by a transfer function G_(I7)(s), which isthe transfer function G_(In)(s) represented by Equation (40) with n=7for the control of the seventh-order harmonic. In other words, theseventh-order harmonic compensator 92″ performs a process represented byEquation (42) shown below, to output seventh-order harmonic compensationsignal Y₇. As for the angular frequency ω₀, a predetermined value is setas an angular frequency for the system voltage fundamental wave, and theintegral gain K_(I7) is a pre-designed value. Also, the seventh-orderharmonic compensator 92″ performs a stability margin maximizationprocess, which includes phase adjustment to correct a phase delay in thecontrol loop for reversing the phase. The seventh-order harmoniccompensator 92″ is also designed by the same method as is thefifth-order harmonic compensator 91″.

$\begin{matrix}{Y_{7} = {{{G_{l\; 7}(s)}I} = {\frac{K_{l\; 7}s}{s^{2} + {49\omega_{0}^{2}}}I}}} & (42)\end{matrix}$

The eleventh-order harmonic compensator 93″ works for suppressing theeleventh-order harmonic. The eleventh-order harmonic compensator 93″performs a process expressed by a transfer function G_(I11)(s), which isthe transfer function G_(In)(s) represented by Equation (40) with n=11for the control of the eleventh-order harmonic. In other words, theeleventh-order harmonic compensator 93″ performs a process representedby Equation (43) shown below, to output eleventh-order harmoniccompensation signal Y₁₁. As for the angular frequency ω₀, apredetermined value is set as an angular frequency for the systemvoltage fundamental wave, and the integral gain K_(I11) is apre-designed value. Also, the eleventh-order harmonic compensator 93″performs a stability margin maximization process, which includes phaseadjustment to correct a phase delay in the control loop for reversingthe phase. The eleventh-order harmonic compensator 93″ is designed bythe same method as is the fifth-order harmonic compensator 91″.

$\begin{matrix}{Y_{11} = {{{G_{l\; 11}(s)}I} = \frac{K_{l\; 11}s}{s^{2} + {121\omega_{0}^{2}}}}} & (43)\end{matrix}$

The fifth-order harmonic compensation signal Y₅ outputted by thefifth-order harmonic compensator 91″, the seventh-order harmoniccompensation signal Y₇ outputted by the seventh-order harmoniccompensator 92″ and the eleventh-order harmonic compensation signal Y₁₁outputted by the eleventh-order harmonic compensator 93″ are addedtogether, and a resulting harmonic compensation signal Y is outputtedfrom the harmonic compensation controller 9″. It should be noted herethat in the present embodiment, description was made for a case wherethe harmonic compensation controller 9″ includes the fifth-orderharmonic compensator 91″, the seventh-order harmonic compensator 92″ andthe eleventh-order harmonic compensator 93″. However, the presentinvention is not limited to this. The harmonic compensation controller9″ is designed in accordance with the orders of harmonics which must besuppressed. For example, if the fifth-order harmonic is the only targetof suppression, then only the fifth-order harmonic compensator 91″ maybe included. Likewise, if it is desired to suppress the thirteenth-orderharmonic, then a thirteenth-order harmonic compensator should be addedfor a process expressed in a matrix G_(I13), which is the transferfunction matrix G_(In)(s) represented by Equation (16), with n=13.

The harmonic compensation signal Y outputted from the harmoniccompensation controller 9″ is added to a correction value signal Xoutputted from the current controller 74′. After the addition of thecompensation signal Y, a system command value K from the systemmatching-fraction generator 72 is added to the correction value signalX, to obtain a command value signal X′, which is then inputted to thePWM signal generator 77′.

The present embodiment provides the same advantages as offered by thetwelfth embodiment. Also, as has been described earlier, the transferfunction G_(I5)(s) is a transfer function which shows a processequivalent to carrying out fixed-to-rotating coordinate conversion, Icontrol and then rotating-to-fixed coordinate conversion. The processperformed in the fifth-order harmonic compensator 91″ is expressed asthe transfer function matrix G_(I5)(s), and therefore is a lineartime-invariant process. Also, the fifth-order harmonic compensation doesnot include nonlinear time-varying processes, i.e., the circuit does notinclude fixed-to-rotating coordinate conversion process norrotating-to-fixed coordinate conversion process. Hence, the entirecontrol loop is a linear time-invariant system. Therefore, thearrangement enables control system design and system analysis using alinear control theory. As described, use of the transfer functionG_(I5)(s) enables to replace the non-linear process in whichfixed-to-rotating coordinate conversion is followed by I control andthen by rotating-to-fixed coordinate conversion with a lineartime-invariant multi-input multi-output system. This makes it easy toperform system analysis and control system design.

The same applies to the seventh-order harmonic compensator 92″ and theeleventh-order harmonic compensator 93″. In other words, the processesperformed in the seventh-order harmonic compensator 92″ and in theeleventh-order harmonic compensator 93″ are also linear time-invariantprocesses, and therefore it is possible to design control systems andperform system analyses using linear control theories.

In the present embodiment, description was made for a case where thefifth-order harmonic compensator 91″, the seventh-order harmoniccompensator 92″ and the eleventh-order harmonic compensator 93″ aredesigned individually from each other. However, the present invention isnot limited to this. The fifth-order harmonic compensator 91″, theseventh-order harmonic compensator 92″ and the eleventh-order harmoniccompensator 93″ may be designed all in one, with a common integral gain.

In the present embodiment, description was made for cases where thefifth-order harmonic compensator 91″, the seventh-order harmoniccompensator 92″ and the eleventh-order harmonic compensator 93″ performa control which replaces I control. However, the present invention isnot limited by this. For example, alternative control which replaces PIcontrol may be provided. If the fifth-order harmonic compensator 91″,the seventh-order harmonic compensator 92″ and the eleventh-orderharmonic compensator 93″ in the present embodiment are to provide analternative control which replaces PI control, it can be accomplished byusing a transfer function G_(PI)n(s) represented by Equation (44) shownbelow which is the transfer function G_(PI)(s) of the element (1, 1) ofthe transfer function matrix G_(PI) expressed by the Equation (11), withω₀ substituted for n·ω₀. Equation (44) provides the element (1, 1) andthe element (2, 2) of the matrix G_(PIn) represented by Equations (35),(35′).

$\begin{matrix}{{G_{P\; \ln}(s)} = \frac{{K_{P}s^{2}} + {K_{l}s} + {K_{P}n^{2}\omega_{0}^{2}}}{s^{2} + {n^{2}\omega_{0}^{2}}}} & (44)\end{matrix}$

If the fifth-order harmonic compensator 91″ is to provide alternativecontrol which replaces PI control, it can be accomplished by using atransfer function G_(PI5)(s) expressed by Equation (44) with n=5. If theseventh-order harmonic compensator 92″ is to provide alternative controlwhich replaces PI control, it can be accomplished by using a transferfunction G_(PI7)(s) expressed by Equation (44) with n=7. If theeleventh-order harmonic compensator 93″ is to provide alternativecontrol which replaces PI control, it can be accomplished by using atransfer function G_(PI11)(s) expressed by Equation (44) with n=11.

Alternatively, the fifth-order harmonic compensator 91″, theseventh-order harmonic compensator 92″ and the eleventh-order harmoniccompensator 93″ may perform an alternative control which replaces theabove-described alternative controls to the I or PI control. Bysubstituting the transfer function F(s) in the transfer functionG_(n)(s) expressed as Equation (45) shown below (which is the transferfunction of the element (1, 1) and the element (2, 2) in the matrix Grepresented by the Equations (23), (23′)) for the transfer functionwhich gives the alternative control, it becomes possible to calculate atransfer function which represents a process equivalent to carrying outfixed-to-rotating coordinate conversion, then the alternative controland then rotating-to-fixed coordinate conversion.

$\begin{matrix}{{G_{n}(s)} = \frac{{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}}{2}} & (45)\end{matrix}$

Like the tenth embodiment, the present embodiment may include adivergence preventer. Also, like the fourth and the fifth embodiments,the output voltage may be controlled. Also, like in the sixthembodiment, the control circuit 12 may be used for a control circuit ofa converter circuit which converts a single-phase AC into DC. Further,the present embodiment may be applied to driving of AC motors as in theeleventh embodiment, for driving single-phase AC motors.

Further, the arrangements in the first, the second, the fourth throughthe eighth, and the eleventh embodiment can also be used to handlesingle-phase applications if their respective control circuits 7 (7′, 8,8′, 10) have their three-phase to two-phase converter 61 replaced withan arrangement for delaying the phase. Hereinafter, a fourteenthembodiment will cover such a case where a single-phase inverter circuitis controlled with the use of a signal which is generated from a currentsignal from the current sensor by delaying the phase by π/2 (90degrees).

FIG. 27 is a block diagram for describing a control circuit according tothe fourteenth embodiment. In this figure, elements which are identicalwith or similar to those in the control circuit 7 (see FIG. 6) accordingto the first embodiment are indicated by the same reference codes.

FIG. 27 shows a control circuit 13 which controls a single-phaseinverter circuit 2″ (see FIG. 25). The control circuit 13 receives asingle-phase current signal detected by the current sensor 5, generatesa PWM signal, and output the PWM signal to the inverter circuit 2″. Thecontrol circuit 13 differs from the control circuit 7 (see FIG. 6)according to the first embodiment in that it does not include thethree-phase to two-phase converter 73 and the two-phase to three-phaseconverter 76, but includes a phase delayer 131.

The phase delayer 131 receives a single-phase current signal detected bythe current sensor 5, and outputs this current signal (alpha axiscurrent signal Iα) and a beta axis current signal Iβ which is made bydelaying the phase of the alpha axis current signal Iα by π/2. The phasedelayer 131 performs a Hilbert transformation in which the phase of theinputted signal is delayed by π/2. The ideal Hilbert transformation isgiven by a transfer function H(ω) represented by Equation (46) shownbelow. In this Equation, ω_(s) is the angular frequency whereas j is theimaginary unit. In other words, the Hilbert transformation is afiltering process in which the amplitude characteristic is kept constantregardless of the frequency, and the phase characteristic is delayed byπ/2 in the positive and the negative frequency regions. Since it isimpossible to implement the ideal Hilbert transformation, it isapproximately implemented as an FIR (Finite impulse response) filter forexample.

$\begin{matrix}{{H(\omega)} = \left\{ \begin{matrix}{{- j},} & {0 < \omega < {\omega_{s}/2}} \\{{+ j},} & {{{- \omega_{s}}/2} < \omega < 0}\end{matrix} \right.} & (46)\end{matrix}$

The phase delayer 131 is not limited to the above, and may beimplemented by any other arrangement as long as the arrangement iscapable of generating a signal with a π/2 phase delay. This can beimplemented, for example, by a complex coefficient filter disclosed inJapanese Patent Application No. 2011-231445 which was filed by theapplicant of the present invention. Another alternative is to use afundamental wave positive phase sequence component extractor F12 whichis related to a seventeenth embodiment to be described later.

The current controller 74 receives deviations ΔIα, ΔIβ of the alpha axiscurrent signal Iα (single-phase current signal detected by the currentsensor 5) and the beta axis current signal Iβ (the signal made bydelaying the phase of the alpha axis current signal Iα by π/2) outputtedby the phase delayer 131 from their respective target values, andperforms a process represented by Equation (13), to generate correctionvalue signals Xα, Xβ for current control. The system command value Kfrom the system matching-fraction generator 72 and the correction valuesignal Xα (or the correction value signal Xβ) from the currentcontroller 74 are added together, to obtain a command value signals X′,which is then inputted to the PWM signal generator 77′. An alternativeprocedure may be that a deviation ΔIα of the alpha axis current signalIα from the alpha axis current target value is calculated first, andthis deviation signal is inputted to the phase delayer 131 to generate asignal which has a π/2 phase delay, and these are inputted to thecurrent controller 74.

In the present embodiment, the phase of a single-phase current signal(alpha axis current signal Iα) is delayed by π/2 whereby a beta axiscurrent signal Iβ is generated instead of performing three-phasetwo-phase conversion to a three-phase current signal in order togenerate the alpha axis current signal Iα and the beta axis currentsignal Iβ. In this way, it is possible to apply the three-phase currentcontrol process according to the first embodiment. The presentembodiment provides the same advantages as offered by the firstembodiment.

It should be noted here that both positive-phase and negative-phasesequence components may be controlled also in the fourteenth embodimentlike in the second embodiment. Further, like in the fourth and the fifthembodiments, output voltage may be controlled. Also, like in the sixthembodiment, the control circuit 13 may be used for a control circuit ofa converter circuit which converts single-phase AC into DC. Stillfurther, the current controller 74 may provide alternative control whichreplaces PI control or other controls. Further, the present embodimentmay be applied to driving of AC motors as in the eleventh embodiment fordriving single-phase AC motors. Still further, like in the sevenththrough the tenth embodiments, the control circuit 12 may include aharmonic compensation controller for suppression of harmonic components.

In the first through the thirteenth embodiments, description was madefor cases where the signal processor according to the present inventionis used as a controller of a control circuit. However, the presentinvention is not limited to this. For example, the signal processoraccording to the present invention may also be used as a filter.

A transfer function of a low-pass filter can be expressed asF(s)=1/(Ts+1), where T represents time constant. Therefore, a transferfunction matrix G_(LPF) which gives a process equivalent to a process inFIG. 28, i.e., the process in which fixed-to-rotating coordinateconversion is followed by low-pass filtering process, and then byrotating-to-fixed coordinate conversion, will be calculated as Equation(47) shown below, by using Equation (10):

$\begin{matrix}\begin{matrix}{G_{LPF} = {{\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}\frac{1}{{TS} + 1} & 0 \\0 & \frac{1}{{TS} + 1}\end{bmatrix}}\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}}} \\{\begin{bmatrix}{\frac{1}{2}\left( {\frac{1}{{T\left( {s + {j\omega}_{0}} \right)} + 1} + \frac{1}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)} & {\frac{1}{2j}\left( {\frac{1}{{T\left( {s + {j\omega}_{0}} \right)} + 1} - \frac{1}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)} \\{{- \frac{1}{2j}}\left( {\frac{1}{{T\left( {s + {j\omega}_{0}} \right)} + 1} - \frac{1}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)} & {\frac{1}{2}\left( {\frac{1}{{T\left( {s + {j\omega}_{0}} \right)} + 1} + \frac{1}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)}\end{bmatrix}} \\{= \begin{bmatrix}\frac{{Ts} + 1}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{- T}\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} \\\frac{T\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{Ts} + 1}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}}\end{bmatrix}}\end{matrix} & (47)\end{matrix}$

FIG. 29 is a Bode diagram for analyzing transfer functions as elementsof the matrix G_(LPF). FIG. 29( a) shows transfer functions of theelement (1, 1) and the element (2, 2) of the matrix GPLF whereas FIG.29( b) shows a transfer function of the element (1, 2) of the matrixG_(PLF), and FIG. 29( c) shows a transfer function of the element (2, 1)of the matrix G_(PLF). FIG. 29 shows a case where the center frequencyis 60 Hz, and the time constant T is set to “0.1”, “1”, “10” and “100”.

All amplitude characteristics in FIGS. 29 (a), (b) and (c) show a peakat the center frequency, and a pass band which decreases as the timeconstant T increases. The amplitude characteristic has a peak at −6 dB(=½). FIG. 29( b) shows a phase characteristic, which attains 0 degreesat the center frequency. In other words, the transfer functions of theelement (1, 1) and the element (2, 2) of the matrix G_(LPF) allowsignals of the center frequency to pass through without changing thephase. FIG. 29( b) shows a phase characteristic, which attains 90degrees at the center frequency. In other words, the transfer functionof the element (1, 2) of the matrix G_(LPF) allows signals of the centerfrequency to pass through with a 90-degree phase advance. On the otherhand, FIG. 29( c) shows a phase characteristic, which attains −90degrees at the center frequency. In other words, the transfer functionsfor the element (2, 1) of the matrix G_(LPF) allows signals of thecenter frequency to pass through with a 90-degree phase delay.Hereinafter, discussion will be made for a process shown in the transferfunction matrix G_(LPF) performed to the alpha axis current signal Iαand the beta axis current signal Iβ (see the vector α and the vector βin FIG. 8) after the three-phase to two-phase conversion.

FIG. 8( a) shows a positive phase sequence component signal of afundamental wave component. The positive phase sequence component in thefundamental wave component of the alpha axis current signal Iα has a90-degree phase advance over the positive phase sequence component inthe fundamental wave component of the beta axis current signal Iβ.Performing the process represented by the transfer function of theelement (1, 1) of the matrix G_(LPF) to the alpha axis current signal Iαhalves the amplitude of the positive phase sequence component in thefundamental wave component and does not change the phase (see FIG. 29(a)). Performing the process represented by the transfer function of theelement (1, 2) in the matrix G_(LPF) to the beta axis current signal Iβhalves the amplitude of the positive phase sequence component in thefundamental wave component and advances the phase by 90 degrees (seeFIG. 29( b)). Therefore, adding the two will extract the positive phasesequence component of the fundamental wave component in the alpha axiscurrent signal Iα. On the other hand, performing the process representedby the transfer function of the element (2, 1) in the matrix G_(LPF) tothe alpha axis current signal Iα halves the amplitude of the positivephase sequence component in the fundamental wave component and delaysthe phase by 90 degrees (see FIG. 29( c)). Performing the processrepresented by the transfer function of the element (2, 2) in the matrixG_(LPF) to the beta axis current signal Iβ halves the amplitude of thepositive phase sequence component in the fundamental wave component anddoes not change the phase. Therefore, adding the two will extract thepositive phase sequence component of the fundamental wave component inthe beta axis current signal Iβ. In other words, the process shown inthe transfer function matrix G_(LPF) is a process to extract thepositive phase sequence component of the fundamental wave component fromthe alpha axis current signal Iα and the beta axis current signal Iβ.

FIG. 8( b) shows a negative phase sequence component signal of afundamental wave component. The negative phase sequence component in thefundamental wave component of the alpha axis current signal Iα has a90-degree phase delay from the negative phase sequence component in thefundamental wave component of the beta axis current signal Iβ.Performing the process represented by the transfer function of theelement (1, 2) of the matrix G_(LPF) to the beta axis current signal Iβadvances the phase of the negative phase sequence component in thefundamental wave component. The advanced phase is now opposite to thephase of the negative phase component in the fundamental wave componentof the alpha axis current signal Iα, so they cancel each other.Performing the process represented by the transfer function of theelement (1, 2) of the matrix G_(LPF) to the alpha axis current signal Iαdelays the phase of the negative-phase sequence component in thefundamental wave component. The delayed phase is now opposite to thephase of the negative phase component in the fundamental wave componentof the alpha axis current signal Iα, so they cancel each other.Therefore, the process shown in the transfer function matrix G_(LPF) isa process to suppress the negative phase sequence component in thefundamental wave component. Also, components other than the fundamentalwave components are attenuated from the level of the fundamental wavecomponent. Therefore, it is clear that the process shown in the transferfunction matrix G_(LPF) is a band-pass filtering process which extractsonly positive phase sequence component in the fundamental wavecomponent. In other words, the matrix transfer function G_(LPF) can beused as a band-pass filter for extracting only positive phase sequencecomponent in the fundamental wave component.

If the negative phase sequence component in the fundamental wavecomponent is to be extracted rather than the positive phase sequencecomponent, it can be achieved by using the transfer function matrixG_(LPF) in which the element (1, 2) and the element (2, 1) are swappedeach other. If both of the positive-phase and the negative-phasesequence components in the fundamental wave component are to beextracted, it can be achieved by using a matrix in which “0” is given tothe element (1, 2) and the element (2, 1) in the transfer functionmatrix G_(LPF).

Hereinafter, description will cover a fifteenth embodiment of thepresent invention, as a case where a signal processor which performs theprocess given by the transfer function matrix G_(LPF) expressed byEquation (47) is used as a band-pass filter in a phase detector.

FIG. 30 shows a block configuration of the phase detector according tothe fifteenth embodiment.

The phase detector F in FIG. 30 detects a phase of a system voltage inan electrical power system for example, and includes a fundamental waveorthogonal component calculator F1 and a phase calculator F2. Thefundamental wave orthogonal component calculator F1 removes unbalancedcomponents (negative phase sequence component in the fundamental wavecomponent) and harmonic components from detected three-phase voltagesignals Vu, Vv, Vw of an electrical power system, and calculates afundamental wave component (sine wave signal) of the normalized voltagesignal, and a signal (cosine wave signal) perpendicular to thefundamental wave component. The phase calculator F2 receives the sinewave signal (momentary value) and the cosine wave signal (momentaryvalue) from the fundamental wave orthogonal component calculator F1 aswell as a phase which is outputted from the phase detector F, to performa PLL operation to output a phase (θ) of the voltage signal in theelectrical power system.

The fundamental wave orthogonal component calculator F1 includes: athree-phase to two-phase converter F11 which converts three-phasevoltage signals Vu, Vv, Vw (momentary values inputted at a predeterminedsampling interval) from an unillustrated voltage sensor into mutuallyperpendicular two-phase (α phase and β phase) alpha axis voltage signalVα and beta axis voltage signal Vβ; a fundamental-wave positive phasesequence component extractor F12 which removes unbalanced components andharmonic components contained in the alpha axis voltage signal Vα andthe beta axis voltage signal Vβ outputted from the three-phase totwo-phase converter F11 thereby extracting the fundamental wavecomponent; and a normalizer F13 which normalizes voltage signals Vr, Vjoutputted from the fundamental wave positive phase sequence componentextractor F12. It should be noted here that the normalizer F13 can beeliminated if appropriate gain adjustment is made to the fundamentalwave positive phase sequence component extractor F12.

The three-phase to two-phase converter F11 is identical with thethree-phase to two-phase converter 83 (see FIG. 13). Generally, thethree-phase voltage signals Vu, Vv, Vw are unbalanced three-phasesignals which contain unbalanced components and odd-order harmoniccomponents such as fifth-order, seventh-order and eleventh-orderharmonics c, in addition to the positive phase sequence component of thefundamental wave component. Therefore, the alpha axis voltage signal Vαand the beta axis voltage signal Vβ outputted from the three-phase totwo-phase converter F11 also contain these components.

The fundamental-wave positive phase sequence component extractor F12extracts voltage signals Vr, Vj which are the positive phase sequencecomponents of the fundamental wave component, from the alpha axisvoltage signal Vα and the beta axis voltage signal Vβ inputted from thethree-phase to two-phase converter F11, by performing a process given bythe transfer function matrix G_(LPF) represented by Equation (47). Byprocessing the alpha axis voltage signal Vα and the beta axis voltagesignal Vβ by fixed-to-rotating coordinate conversion based on the phaseθ of the system voltage fundamental wave, the positive phase sequencecomponent in the fundamental wave component is converted into a DCcomponent. The signals after the fixed-to-rotating coordinate conversionare then processed with a low-pass filter which allows only the DCcomponent to pass through while blocking AC components. As a result,only the positive phase sequence component in the fundamental wavecomponent which was converted into DC is extracted. The extracted DCcomponent is subjected to rotating-to-fixed coordinate conversion,whereby the DC component is brought back to the positive phase sequencecomponent of the fundamental wave component. In this way, the positivephase sequence component of the fundamental wave component, i.e., thevoltage signals Vr, Vj are extracted. The fundamental-wave positivephase sequence component extractor F12 performs a process which isequivalent to the above-described processes, as a linear time-invariantprocess.

The fundamental-wave positive phase sequence component extractor F12performs a process represented by Equation (48) shown below. As for theangular frequency ω₀, a predetermined value is set as an angularfrequency ω₀=120π [rad/sec] correspondingly to the system frequencyfs=60 Hz, and the time constant T is a pre-designed value.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{Vr} \\{Vj}\end{bmatrix} = {G_{LPF}\begin{bmatrix}{V\; \alpha} \\{V\; \beta}\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{{Ts} + 1}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{- T}\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} \\\frac{T\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{Ts} + 1}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}}\end{bmatrix}\begin{bmatrix}{V\; \alpha} \\{V\; \beta}\end{bmatrix}}}\end{matrix} & (48)\end{matrix}$

It should be noted here that the angular frequency to used in thefundamental-wave positive phase sequence component extractor F12 neednot necessarily be pre-designed. If the signal process makes signalsampling at a fixed interval, then a system frequency fs may be detectedby, e.g., a frequency detector so that the angular frequency ω₀ iscalculated from the detected frequency.

The normalizer F13 performs an arithmetic process of normalizing thelevel of voltage signals Vr, Vj which are outputted from thefundamental-wave positive phase sequence component extractor F12 to “1”.Since the voltage signals Vr, Vj outputted from the fundamental-wavepositive phase sequence component extractor F12 are a sine wave signaland a cosine wave signal having the same amplitude, the amplitude isobtained by calculating √(Vr²+Vj²). Therefore, the normalizer F13performs processes Vr/√(Vr2+Vj2) and Vj/√(Vr2+Vj2) to the voltagesignals Vr, Vj respectively, thereby normalizing the signals, and thenoutputs normalized signals represented by a voltage signalVr′=cos(θ)(θ=ω·t) and a voltage signal Vj′=sin(θ).

The phase calculator F2 receives the normalized voltage signals Vr′, Vj′from the fundamental wave the orthogonal component calculator F1 and aphase θ′ (hereinafter will be called “output phase θ′”) from the phasecalculator F2, calculates a phase difference Δθ(=θ−θ′) between the phaseθ (hereinafter will be called “input phase θ”) of the voltage signalsVr′, Vj′ and the output phase θ′, updates the output phase θ′ based onthe phase difference Δθ, and thereby converges the output phase θ′ onthe input phase θ. However, the configuration of the phase calculator F2is not limited to the one described above. For example, the phasedifference may be calculated by a different method.

As understood from the above, according to the phase detector F in thepresent embodiment, the fundamental-wave positive phase sequencecomponent extractor F12 extracts the positive phase sequence componentof the fundamental wave component, removes the other components(unbalanced component and harmonic components of the predeterminedorder(s)) and thereafter calculates the phase difference Δθ. Therefore,the phase detector F can detect the phase quickly and accurately whilereducing influence of unbalanced components and harmonic components.Also, the phase detector F provides another advantage that there is nophase difference between the input to and the output from thefundamental-wave positive phase sequence component extractor F12.Further, since the phase detector also reduces noise frequencycomponents added through the voltage sensor for example, there is noneed for providing a filter.

As has been described earlier, the transfer function matrix G_(LPF) is atransfer function matrix which represents a process equivalent tocarrying out fixed-to-rotating coordinate conversion, low-pass filterprocess and then rotating-to-fixed coordinate conversion. The processperformed in the fundamental-wave positive phase sequence componentextractor F12 is expressed as the matrix G_(LPF) of the transferfunction, and therefore is a linear time-invariant process. Therefore,the arrangement enables control system design and system analysis usinga linear control theory.

In the fifteenth embodiment, description was made for a case where asignal processor according to the present invention is used as aband-pass filter incorporated in a phase detector. However the presentinvention is not limited to this. The signal processor according to thepresent invention can also be used as a band-pass filter whichexclusively extract positive phase sequence component or negative phasesequence component from a signal of a specific frequency. Also, thesignal processor according to the present invention can be used as aband-pass filter which extracts both positive-phase and negative-phasesequence components from a signal of a specific frequency.

In the fifteenth embodiment, description was made for a case where thefundamental-wave positive phase sequence component extractor F12performs alternative process which replaces a low-pass filter, therebyextracting positive phase sequence component of the fundamental wavecomponent. However, the present invention is not limited to this. Ifunbalanced components or harmonic components as targets of suppressionare known, those components may be suppressed so as to extract thepositive phase sequence component of the fundamental wave component. Inthis case, the signal processor may be designed to provide a processwhich replaces a high-pass filter, so that the signal processor can beused as a notch filter. Hereinafter, description will cover a sixteenthembodiment, where the fundamental-wave positive phase sequence componentextractor F12 performs a process which replaces a high-pass filter, toextract a fundamental wave component.

A transfer function of a high-pass filter can be expressed asF(s)=Ts/(Ts+1), where T represents time constant. Therefore, a transferfunction matrix G_(HPF) which represents a process equivalent to theprocess in FIG. 31, in which fixed-to-rotating coordinate conversion isfollowed by a high-pass filter process, and then followed by arotating-to-fixed coordinate conversion, will be calculated as Equation(49) shown below by using Equation (10).

$\begin{matrix}\begin{matrix}{G_{HPF} = {{\begin{bmatrix}{\cos \; \theta} & {\sin \; \theta} \\{{- \sin}\; \theta} & {\cos \; \theta}\end{bmatrix}\begin{bmatrix}\frac{Ts}{{TS} + 1} & 0 \\0 & \frac{Ts}{{TS} + 1}\end{bmatrix}}\begin{bmatrix}{\cos \; \theta} & {{- \sin}\; \theta} \\{\sin \; \theta} & {\cos \; \theta}\end{bmatrix}}} \\{\begin{bmatrix}{\frac{1}{2}\left( {\frac{T\left( {s + {j\omega}_{0}} \right)}{{T\left( {s + {j\omega}_{0}} \right)} + 1} + \frac{T\left( {s - {j\omega}_{0}} \right)}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)} & {\frac{1}{2j}\left( {\frac{T\left( {s + {j\omega}_{0}} \right)}{{T\left( {s + {j\omega}_{0}} \right)} + 1} - \frac{T\left( {s - {j\omega}_{0}} \right)}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)} \\{{- \frac{1}{2j}}\left( {\frac{T\left( {s + {j\omega}_{0}} \right)}{{T\left( {s + {j\omega}_{0}} \right)} + 1} - \frac{T\left( {s - {j\omega}_{0}} \right)}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)} & {\frac{1}{2}\left( {\frac{T\left( {s + {j\omega}_{0}} \right)}{{T\left( {s + {j\omega}_{0}} \right)} + 1} + \frac{T\left( {s - {j\omega}_{0}} \right)}{{T\left( {s - {j\omega}_{0}} \right)} + 1}} \right)}\end{bmatrix}} \\{= \begin{bmatrix}\frac{{T^{2}s^{2}} + {Ts} + {T^{2}\omega_{0}^{2}}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{T\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} \\\frac{T\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{T^{2}s^{2}} + {Ts} + {T^{2}\omega_{0}^{2}}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}}\end{bmatrix}}\end{matrix} & (49)\end{matrix}$

FIG. 32 is a Bode diagram for analyzing transfer functions as elementsof a matrix G_(HPF). FIG. 32( a) shows transfer functions of the element(1, 1) and the element (2, 2) of the matrix G_(HPF) whereas FIG. 32( b)shows a transfer function of the element (1, 2) of the matrix G_(HPF),and FIG. 32( c) shows a transfer function of the element (2, 1) of thematrix G_(HPF). FIG. 32 shows a case where the center frequency is 60Hz, and the time constant T is set to “0.1”, “1”, “10” and “100”.

FIG. 32( a) shows an amplitude characteristic, with an attenuation nearthe center frequency. The amplitude characteristic at the centerfrequency is −6 dB(=½). The figure also shows a narrowing cut-off bandas the time constant T increases. FIGS. 32 (b) and (c) both show anamplitude characteristic which has a peak at the center frequency, at −6dB(=½). The figure also shows a narrowing pass band as the time constantT increases. Also, FIG. 32( a) shows a phase characteristic, whichattains zero degree at the center frequency. In other words, thetransfer functions of the element (1, 1) and the element (2, 2) of thematrix G_(HPF) allow signals of the center frequency to pass throughwithout changing the phase. FIG. 32( b) shows a phase characteristic,which attains −90 degrees at the center frequency. In other words, thetransfer functions for the element (1, 2) of the matrix G_(HPF) allowssignals of the center frequency to pass through with a 90-degree phasedelay. On the other hand, FIG. 32( c) shows a phase characteristic,which attains 90 degrees at the center frequency. In other words, thetransfer functions for the element (2, 1) of the matrix G_(HPF) allowssignals of the center frequency to pass through with a 90-degree phaseadvance. Hereinafter, discussion will be made for a process expressed bythe transfer function matrix G_(HPF) to be performed to the alpha axisvoltage signal Vα and the beta axis voltage signal Vβ (see the vector αand the vector β in FIG. 8) which are outputted from the three-phase totwo-phase converter F11.

The positive phase sequence component in the fundamental wave componentof the alpha axis voltage signal Vα has a 90-degree phase advance overthe positive phase sequence component in the fundamental wave componentof the beta axis voltage signal Vβ. Performing the process representedby the transfer function of the element (1, 1) of the matrix G_(HPF) tothe alpha axis voltage signal Vα halves the amplitude of the positivephase sequence component in the fundamental wave component and does notchange the phase (see FIG. 32( a)). Performing the process representedby the transfer function of the element (1, 2) of the matrix G_(HPF) tothe beta axis voltage signal Vβ halves the amplitude of the positivephase sequence component in the fundamental wave component and delaysthe phase by 90 degrees (see FIG. 32( b)). Therefore, the two phasesbecomes opposite to each other, which means they cancel each other whenthe two are added to each other. On the other hand, performing theprocess represented by the transfer function of the element (2, 1) inthe matrix G_(HPF) to the alpha axis voltage signal Vα halves theamplitude of the positive phase sequence component in the fundamentalwave component and advances the phase by 90 degrees (see FIG. 32( c)).Performing the process represented by the transfer function of theelement (2, 2) in the matrix G_(HPF) to the beta axis voltage signal Vβhalves the amplitude of the positive phase sequence component in thefundamental wave component and does not change the phase. Therefore, thetwo phases becomes opposite to each other, which means they cancel eachother when the two are added to each other.

The negative phase sequence component in the fundamental wave componentof the alpha axis voltage signal Vα has a 90-degree phase delay from thenegative phase sequence component in the fundamental wave component ofthe beta axis voltage signal Vβ. Performing the process represented bythe transfer function of the element (1, 1) of the matrix G_(HPF) to thealpha axis voltage signal Vα halves the amplitude of the negative-phasesequence component in the fundamental wave component and does not changethe phase. Performing the process represented by the transfer functionof the element (1, 2) of the matrix G_(HPF) to the beta axis voltagesignal Vβ halves the amplitude of the negative-phase sequence componentin the fundamental wave component and delays the phase by 90 degrees.Therefore, both phases are now the same as the phase of the negativephase sequence component in the fundamental wave component of the alphaaxis voltage signal Vα, which means adding the two will reproduce thenegative phase sequence component in the fundamental wave component ofthe alpha axis voltage signal Vα. On the other hand, performing theprocess represented by the transfer function of the element (2, 1) inthe matrix G_(HPF) to the alpha axis voltage signal Vα halves theamplitude of the negative-phase sequence component in the fundamentalwave component and advances the phase by 90 degrees (see FIG. 18( c)).Performing the process represented by the transfer function of theelement (2, 2) in the matrix G_(HPF) to the beta axis voltage signal Vβhalves the amplitude of the negative phase sequence component in thefundamental wave component and does not change the phase. Therefore,both phases are now the same as the phase of the beta axis voltagesignal Vβ, which means adding the two will reproduce the negative phasesequence component in the fundamental wave component of the beta axisvoltage signal Vβ.

In other words, the transfer function matrix G_(HPF) allows the negativephase sequence component of the fundamental wave component to passthrough while suppressing the positive phase sequence component of thefundamental wave component. For signals other than the positive phasesequence component and the negative phase sequence component of thefundamental wave component (e.g., harmonic component signals), theprocess represented by the transfer function of the element (1, 1) andthe element (2, 2) of the matrix G_(HPF) allows these signals to passthrough (see FIG. 32( a)) as they are whereas the process represented bythe transfer function of the element (1, 2) and the element (2, 1)allows these signals to pass through with some attenuation butsubstantially as they are (see FIGS. 32( b), (c)). Therefore, theprocess shown in the transfer function matrix G_(HPF) is a notchfiltering process which suppresses only the positive phase sequencecomponent in the fundamental wave component.

Swapping the element (1, 2) and the element (2, 1) in the transferfunction matrix G_(HPF) will result in the opposite of what wasdescribed above, i.e., negative phase sequence components in thefundamental wave component will be suppressed while positive phasesequence component, harmonic components, etc. in the fundamental wavecomponent will be allowed to pass through. In other words, if theelement (1, 2) and the element (2, 1) in the matrix G_(HPF) of thetransfer function is swapped with each other, the resulting process is anotch filtering process which suppresses only the negative phasesequence component in the fundamental wave component. The matrix mayalso be considered as the transfer function matrix G_(HPF) in which theangular frequency ω₀ is substituted for “−ω₀”. In other words, theprocess shown in the transfer function matrix G_(HPF) is a notchfiltering process which suppresses only a designated frequency componentspecified as having an angular frequency ω₀.

For example, if it is desired to suppress the negative phase component(−fs), the fifth-, the seventh- and the eleventh-order harmoniccomponents (−5 fs, +7 fs, −11 fs) in the fundamental wave component, thenotch filtering process may be performed to each of these frequencycomponents in order to extract only the positive phase sequencecomponent of the fundamental wave component.

The phase detector according to the sixteenth embodiment can berepresented by the block diagram of the phase detector F according tothe fifteenth embodiment shown in FIG. 30, differing, however, in thatthe fundamental-wave positive phase sequence component extractor F12 isreplaced by a fundamental-wave positive phase sequence componentextractor F12′ (see FIG. 33 to be described later) (The figure onlyshows the fundamental-wave positive phase sequence component extractorF12′ and none other). For an identification purpose from the phasedetector F according to the fifteenth embodiment, the phase detectoraccording to the sixteenth embodiment will be denoted as a phasedetector F′.

FIG. 33 is a block diagram for describing an internal configuration of afundamental-wave positive phase sequence component extractor F12′according to the sixteenth embodiment.

The fundamental-wave positive phase sequence component extractor F12′includes a negative phase sequence component remover F121, a fifth-orderharmonic remover F122, a seventh-order harmonic remover F123, and aneleventh-order harmonic remover F124. The negative phase sequencecomponent remover F121 suppresses negative phase sequence componentsignals by removing a negative phase sequence component from an alphaaxis voltage signal Vα and a beta axis voltage signal Vβ inputted fromthe three-phase to two-phase converter F11 (see FIG. 30). The negativephase sequence component remover F121 performs a process in which theangular frequency ω₀ is substituted for “−ω₀” in the transfer functionmatrix G_(LPF) represented by Equation (48) described above; namely itperforms a process expressed by Equation (50) shown below, where Vα′,Vβ′ are signals outputted from the negative phase sequence componentremover F121. As for the angular frequency ω₀, a predetermined value isset as an angular frequency ωs=120π [rad/sec] correspondingly to thesystem frequency fs=60 Hz, and the time constant T is a pre-designedvalue.

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{V\; \alpha^{\prime}} \\{V\; \beta^{\prime}}\end{bmatrix} = {\begin{bmatrix}\frac{{T^{2}s^{2}} + {Ts} + {T^{2}\left( {- \omega_{0}} \right)}^{2}}{\left( {{Ts} + 1} \right)^{2} + \left( {{- T}\; \omega_{0}} \right)^{2}} & \frac{T\; \left( {- \omega_{0}} \right)}{\left( {{Ts} + 1} \right)^{2} + \left( {{- T}\; \omega_{0}} \right)^{2}} \\\frac{{- T}\; \left( {- \omega_{0}} \right)}{\left( {{Ts} + 1} \right)^{2} + \left( {{- T}\; \omega_{0}} \right)^{2}} & \frac{{T^{2}s^{2}} + {Ts} + {T^{2}\left( {- \omega_{0}} \right)}^{2}}{\left( {{Ts} + 1} \right)^{2} + \left( {{- T}\; \omega_{0}} \right)^{2}}\end{bmatrix}\begin{bmatrix}{V\; \alpha} \\{V\; \beta}\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{{T^{2}s^{2}} + {Ts} + {T^{2}\omega_{0}^{2}}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{- T}\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} \\\frac{T\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{T^{2}s^{2}} + {Ts} + {T^{2}\omega_{0}^{2}}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}}\end{bmatrix}\begin{bmatrix}{V\; \alpha} \\{V\; \beta}\end{bmatrix}}}\end{matrix} & (50)\end{matrix}$

The fifth-order harmonic remover F122, the seventh-order harmonicremover F123 and the eleventh-order harmonic remover F124 suppress thefifth-order harmonic, the seventh-order harmonic and the eleventh-orderharmonic respectively by performing processes where the angularfrequency ω₀ is substituted for “−5ω₀”, “7ω₀” and “−11ω₀” respectivelyin the transfer function matrix G_(HPF) represented by Equation (49). Asfor the angular frequency ω₀, a predetermined value is set as an angularfrequency ωs=120π [rad/sec] correspondingly to the system frequencyfs=60 Hz.

It should be noted here that the angular frequency ω₀ used in thefundamental-wave positive phase sequence component extractor F12′ neednot necessarily be pre-designed. If the signal process makes signalsampling at a fixed interval, then a system frequency fs may be detectedby, e.g., a frequency detector so that the angular frequency ω₀ iscalculated from the detected frequency.

FIG. 34 shows a frequency characteristic of the fundamental-wavepositive phase sequence component extractor F12′. The negative phasesequence component remover F121, the fifth-order harmonic remover F122,the seventh-order harmonic remover F123 and the eleventh-order harmonicremover F124 have frequency characteristics to suppress the negativephase sequence component (−fs), the fifth-order harmonic component (−5fs), the seventh-order harmonic component (7 fs) and the eleventh-orderharmonic component (−11 fs) respectively. Therefore, a frequencycharacteristic of the fundamental-wave positive phase sequence componentextractor F12′ as a whole is as shown in FIG. 34. According to thefigure, the negative phase sequence component (−fs), the fifth-orderharmonic component (−5 fs), the seventh-order harmonic component (7 fs)and the eleventh-order harmonic component (−11 fs) are suppressed whilethe other component, i.e., the fundamental wave component (fs) isallowed to pass. Therefore, the fundamental-wave positive phase sequencecomponent extractor F12′ allows the positive phase sequence component ofthe fundamental wave component to desirably pass through, and therebyextracts the positive phase sequence component voltage signals Vr, Vj ofthe fundamental wave component from the alpha axis voltage signal Vα andbeta axis voltage signal Vβ.

Generally, harmonics which are found in an electrical power system arethe fifth-order, the seventh-order and the eleventh-order harmonics.Thus, the present embodiment is designed to suppress these and thenegative phase sequence components in the fundamental wave component.The fundamental-wave positive phase sequence component extractor F12′ isdesigned in accordance with the orders of harmonics which must besuppressed. For example, if the fifth-order harmonic is the onlyharmonic to be suppressed, there is no need to include the seventh-orderharmonic remover F123 or the eleventh-order harmonic remover F124. If itis desired to further suppress the thirteenth-order harmonic, athirteenth-order harmonic remover should simply be added with theangular frequency ω₀ substituted for “13ω₀” in the transfer functionmatrix G_(HPF) of the transfer function represented by Equation (49).Also, if harmonic components in the electrical power system arenegligibly small, the remover may only include the negative phasesequence component remover F121. Further, if there is a noise added bythe voltage sensor for example, the fundamental-wave positive phasesequence component extractor F12′ may also include a noise remover forremoving the noise component of that specific frequency.

Again in the sixteenth embodiment, it is possible to extract thepositive phase sequence component of the fundamental wave component byremoving negative phase sequence component and harmonic components ofthe predetermined orders in the fundamental wave component by using thefundamental-wave positive phase sequence component extractor F12′.Therefore, the embodiment provides the same advantages as does thefifteenth embodiment.

As already known publicly, multi-stage configuration of notch filtersand band-pass filters will provide sharp filtering characteristics whileit is easy to adjust removal characteristics of the negative phasesequence component and harmonic components as well as to adjustresponsiveness. In practical application therefore, it is recommendableto make use of multi-stage configuration of an appropriate number ofstages. For example, the phase detector F (see FIG. 30) according to thefifteenth embodiment may further include another fundamental-wavepositive phase sequence component extractor F12 after thefundamental-wave positive phase sequence component extractor F12. Also,a combination of notch filters and band-pass filters will provide anadvantage of combined characteristics of the two types, providing anoption when faster and more accurate phase detection are required.Therefore, for example, the phase detector F (see FIG. 30) according tothe fifteenth embodiment may further include a fundamental-wave positivephase sequence component extractor F12′ after the fundamental-wavepositive phase sequence component extractor F12.

In the sixteenth embodiment, description was made for a case where asignal processor according to the present invention is used as a notchfilter incorporated in a phase detector. However the present inventionis not limited to this. The signal processor according to the presentinvention can also be used as a notch filter which exclusivelysuppresses positive phase sequence components or negative phase sequencecomponents from a signal of a specific frequency.

In the fifteenth and the sixteenth embodiment, description was made forcases where the phase detector F (F′) detects phases of a system voltagein a three-phase electrical power system. However, the present inventionis also applicable to cases where a phase of a system voltage in asingle-phase electrical power system is detected. Hereinafter, aseventeenth embodiment will provide a phase detector which detects asystem voltage in a single-phase electrical power system.

FIG. 35 is a block diagram of a phase detector F″ according to theseventeenth embodiment. The phase detector F″ differs from the phasedetector F in FIG. 30 only in that it does not include the three-phaseto two-phase converter F11. Since single-phase power has only onevoltage signal V, a sampling data of this voltage signal V and “0” areinputted to the fundamental-wave positive phase sequence componentextractor F12. With Vα=V and Vβ=0, Equation (48) shown above will beexpressed as Equation (51) below:

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{Vr} \\{Vj}\end{bmatrix} = {G_{LPF}\begin{bmatrix}V \\0\end{bmatrix}}} \\{= {\begin{bmatrix}\frac{{Ts} + 1}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{- T}\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} \\\frac{T\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}} & \frac{{Ts} + 1}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}}\end{bmatrix}\begin{bmatrix}V \\0\end{bmatrix}}} \\{= \begin{bmatrix}{\frac{{Ts} + 1}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}}V} \\{\frac{T\; \omega_{0}}{\left( {{Ts} + 1} \right)^{2} + \left( {T\; \omega_{0}} \right)^{2}}V}\end{bmatrix}}\end{matrix} & (51)\end{matrix}$

Performing a process represented by the transfer function of the element(1, 1) of the matrix GLPF to the voltage signal V halves the amplitudeof the fundamental wave component and does not change the phase (seeFIG. 29( a)). In other words, the voltage signal Vr is the voltagesignal V having its amplitude halved. Performing the process representedby the transfer function of the element (2, 1) of the matrix G_(LPF) tothe voltage signal V halves the amplitude of the fundamental wavecomponent and delays the phase by 90 degrees (see FIG. 29( c)). In otherwords, the voltage signal Vj is the voltage signal V having itsamplitude halved and its phase delayed by 90 degrees. Therefore, withthe input of the voltage signal V and “0”, the fundamental-wave positivephase sequence component extractor F12 outputs orthogonal voltagesignals Vr, Vj. It should be noted here that although the amplitude ofthe voltage signals Vr, Vj is a half of the amplitude of the fundamentalwave component in the voltage signal V, it is normalized by thenormalizer F13. The phase detector F in FIG. 30 may not have thethree-phase to two-phase converter F11, but have an arrangement that asampling data of one of the phases U, V, W in the voltage signal V isinputted.

In the fundamental-wave positive phase sequence component extractor F12,an input of a single-phase voltage signal results in an output ofmutually perpendicular voltage signals Vr, Vj (sine wave signal andcosine wave signal) like in a three-phase configuration. Therefore, thefundamental-wave positive phase sequence component extractor F12, thenormalizer F13 and the phase calculator F2 can be implemented in thesame way as is the three-phase phase detector F in FIG. 30. Theseventeenth embodiment provides the same advantages as offered by thefifteenth embodiment.

In the seventeenth embodiment, description was made for a case where asignal processor according to the present invention is used as a filterincorporated in a phase detector. However the present invention is notlimited to this. The signal processor according to the present inventioncan also be used as a filter which exclusively extracts signals of aspecific frequency from an input signal, and outputs mutuallyperpendicular two signals. This, for example, may be used in a controlcircuit of a single-phase inverter circuit, or may used in the phasedelayer 131 according to the fourteenth embodiment. It should be notedhere that as has been described earlier, performing the process given bythe matrix G_(LPF) to a single-phase signal will halve the amplitude ofthe original signal's fundamental wave component in the outputtedsignal, and therefore it is necessary to provide an arrangement todouble the amplitude of the outputted signal.

The signal processors, filters, control circuits, according to thepresent invention and interconnection inverter systems and PWM convertersystems using these control circuits are not limited to those alreadycovered by the embodiments. Specific arrangements in the signalprocessors, filters, control circuits, and interconnection invertersystems and PWM converter systems using these control circuits accordingto the present invention may be varied in many ways.

1-30. (canceled)
 31. A signal processor with a signal processingfunction corresponding to that of a conventional signal processingapparatus configured to process input signals based on at least apredetermined transfer function F(s), the signal processor comprising: afirst input portion for receiving a first input signal; and a signalprocessing unit for processing the first input signal based on at leasta first transfer function G_(I)(s); wherein the first transfer functionG_(I)(s) is expressed by a formula including at least F(s+jnω₀) andF(s−jnω₀), where j represents an imaginary unit, n represents a positiveinteger, and ω₀ represents a non-zero angular frequency relating to thesignal processor.
 32. The signal processor according to claim 31,wherein the first transfer function G₁(s) is equal to:$\frac{1}{2}{\left\{ {{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}} \right\}.}$33. The signal processor according to claim 32, further comprising asecond input portion for receiving a second input signal, wherein thesignal processing unit is configured to: generate a first processsignal, a second process signal and a first output signal, the firstprocess signal being generated by processing the first input signalbased on the first transfer function G₁(s), the second process signalbeing generated by processing the second input signal based on a secondtransfer function G₂(s), the first output signal being generated byadding the first process signal and the second process signal; andgenerate a third process signal, a fourth process signal and a secondoutput signal, the third process signal being generated by processingthe first input signal based on a third transfer function G₃(s), thefourth process signal being generated by processing the second inputsignal based on the first transfer function G₁(s), the second outputsignal being generated by adding the third process signal and the fourthprocess signal; wherein the second transfer function G₂(s) is equal to:${{\pm \frac{1}{2j}}\left\{ {{F\left( {s + {j\; n\; \omega_{0}}} \right)} - {F\left( {s - {j\; n\; \omega_{0}}} \right)}} \right\}},$and the third transfer function G₃(s) is equal to:${\mp \frac{1}{2j}}{\left\{ {{F\left( {s + {j\; n\; \omega_{0}}} \right)} - {F\left( {s - {j\; n\; \omega_{0}}} \right)}} \right\}.}$34. The signal processor according to claim 31, further comprising asecond input portion for receiving a second input signal, and a thirdinput portion for receiving a third input signal, wherein the signalprocessing unit is configured to: generate a first process signal, asecond process signal, a third process signal and a first output signal,the first process signal being generated by processing the first inputsignal based on the first transfer function G₁(s), the second processsignal being generated by processing the second input signal based on asecond transfer function G₂(s), the third process signal being generatedby processing the third input signal based on the second transferfunction G₂(s), the first output signal being generated by adding thefirst process signal, the second process signal and the third processsignal; generate a fourth process signal, a fifth process signal and asecond output signal, the fourth process signal being generated byprocessing the first input signal based on the second transfer functionG₂(s), the fifth process signal being generated by processing the secondinput signal based on the first transfer function G₁(s), the secondoutput signal being generated by adding the third process signal, thefourth process signal and the fifth process signal; and generate a sixthprocess signal and a third output signal, the sixth process signal beinggenerated by processing the third input signal based on the firsttransfer function G₁(s), the third output signal being generated byadding the second process signal, the fourth process signal and thesixth process signal; wherein the first transfer function G₁(s) is equalto:${\frac{1}{3}\left\{ {{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}} \right\}},$and the second transfer function G₂(s) is equal to:${- \frac{1}{6}}{\left\{ {{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}} \right\}.}$35. The signal processor according to claim 31, further comprising asecond input portion for receiving a second input signal, and a thirdinput portion for receiving a third input signal, wherein the signalprocessing unit is configured to: generate a first process signal, asecond process signal, a third process signal and a first output signal,the first process signal being generated by processing the first inputsignal based on the first transfer function G₁(s), the second processsignal being generated by processing the second input signal based on asecond transfer function G₂(s), the third process signal being generatedby processing the third input signal based on a third transfer functionG₃(s), the first output signal being generated by adding the firstprocess signal, the second process signal and the third process signal;generate a fourth process signal, a fifth process signal, a sixthprocess signal and a second output signal, the fourth process signalbeing generated by processing the first input signal based on the thirdtransfer function G₃(s), the fifth process signal being generated byprocessing the second input signal based on the first transfer functionG₁(s), the sixth process signal being generated by processing the thirdinput signal based on the second transfer function G₂(s), the secondoutput signal being generated by adding the fourth process signal, thefifth process signal and the sixth process signal; and generate aseventh process signal, an eighth process signal, a ninth process signaland a third output signal, the seventh process signal being generated byprocessing the first input signal based on the second transfer functionG₂(s), the eighth process signal being generated by processing thesecond input signal based on the third transfer function G₃(s), theninth process signal being generated by processing the third inputsignal based on the first transfer function G₁(s), the third outputsignal being generated by adding the seventh process signal, the eighthprocess signal and the ninth process signal; wherein the first transferfunction G₁(s) is equal to:${\frac{1}{3}\left\{ {{F\left( {s + {j\; n\; \omega_{0}}} \right)} + {F\left( {s - {j\; n\; \omega_{0}}} \right)}} \right\}},$the second transfer function G₂(s) is equal to:${\frac{1}{6}\left\{ {{\left( {{- 1} \mp {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; n\; \omega_{0}}} \right)}} + {\left( {{- 1} \pm {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; n\; \omega_{0}}} \right)}}} \right\}},$and the third transfer function G₃(s) is equal to:$\frac{1}{6}{\left\{ {{\left( {{- 1} \pm {\sqrt{3}j}} \right) \cdot {F\left( {s + {j\; n\; \omega_{0}}} \right)}} + {\left( {{- 1} \mp {\sqrt{3}j}} \right) \cdot {F\left( {s - {j\; n\; \omega_{0}}} \right)}}} \right\}.}$36. A control circuit for controlling a plurality of switching unitsinside a power converter circuit by a PWM signal, the control circuitcomprising: a signal processor according to claim 31; and a PWM signalgenerator; wherein the signal processor is configured to receive aninput signal based on an output from or an input to the power convertercircuit, and also to generate an output signal in response to the inputsignal, wherein the PWM signal generator is configured to generate a PWMsignal based on the output signal from the signal processor.
 37. Thecontrol circuit according to claim 36, further comprising a two-phaseconversion unit for conversion of an input signal based on an outputfrom or an input to the power converter circuit into a first signal anda second signal.
 38. The control circuit according to claim 37, whereinthe power converter circuit relates to a three-phase alternate current,and the two-phase conversion unit converts an input signal based on athree-phase output from or a three-phase input to the power convertercircuit into the first signal and the second signal.
 39. The controlcircuit according to claim 37, wherein the power converter circuitrelates to a single-phase alternate current, and the two-phaseconversion unit generates a signal, as the above-mentioned first signal,based on a single-phase output from or a single-phase input to the powerconverter circuit, while also generating a signal, as theabove-mentioned second signal, having a 90-degree phase delay withrespect to the first signal.
 40. The control circuit according to claim37, further comprising a first deviation signal generator and a seconddeviation signal generator, wherein the first deviation signal generatorgenerates a first deviation signal based on the above-mentioned firstsignal and a predetermined target value, the second deviation signalgenerator generates a second deviation signal based on theabove-mentioned second signal and a predetermined target value, thefirst deviation signal and the second deviation signal being input tothe signal processor.
 41. The control circuit according to claim 37,further comprising a divergence determination unit and an output controlunit, wherein the divergence determination unit is configured todetermine, based on the output signal from the signal processor, ifcontrol for driving the plurality of switching units tends to diverge,and wherein when the divergence determination unit determines that thecontrol for driving the plurality of switching units tends to diverge,the output control unit stops the output signal or changes a phase ofthe output signal to another phase whereby the control for driving theplurality of switching units does not diverge.
 42. The signal processoraccording to claim 31, wherein the transfer function F(s) is equal toK_(I)/s, where K_(I) represents an integral gain.
 43. The signalprocessor according to claim 31, wherein the transfer function F(s) isequal to K_(P)+K_(I)/s, where K_(P) and K_(I) represent a proportionalgain and an integral gain, respectively.
 44. The control circuitaccording to claim 36, wherein the power converter circuit comprises aninverter circuit for generation of AC power to be supplied to anelectrical power system, and the angular frequency ω₀ is an angularfrequency of a fundamental wave in the electrical power system.
 45. Thecontrol circuit according to claim 36, wherein the power convertercircuit comprises an inverter circuit for driving a motor, and theangular frequency ω₀ corresponds to a rotating speed of the motor. 46.The control circuit according to claim 37, wherein the power convertercircuit comprises a converter circuit for conversion of AC powersupplied from an electrical power system into DC power, and the angularfrequency ω₀ corresponds to an angular frequency of a fundamental wavein the electrical power system.
 47. An interconnection inverter systemcomprising: an inverter circuit; and a control circuit according toclaim
 44. 48. A PWM converter system comprising: a converter circuit;and a control circuit according to claim
 46. 49. A filter comprising asignal processor according to claim 31, wherein the transfer functionF(s) is equal to 1/(T·s+1) or T·s/(T·s+1), where T represents a timeconstant.
 50. A phase detector for detecting a phase of a fundamentalwave component in an AC signal, the phase detector comprising a filteraccording to claim 49, wherein the angular frequency ω₀ is an angularfrequency of a fundamental wave component in the AC signal.